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# Complex number exponential form

### Video: Complex Numbers in Exponential Form - analyzemath

1. Complex numbers in exponential form are easily multiplied and divided. The power and root of complex numbers in exponential form are also easily computed Multiplication of Complex Numbers in Exponential Forms Let $$z_1 = r_1 e^{ i \theta_1}$$ and $$z_2 = r_2 e^{ i \theta_2}$$ be complex numbers in exponential form
2. Complex Numbers in Exponential Form Bernd Schroder¨ Bernd Schroder¨ Louisiana Tech University, College of Engineering and Science Complex Numbers in Exponential Form
3. d you of the rules for adding or subtracting exponents when multiplying or dividing exponentials: x m · x n = x m + n and x m / x n = x m − n

Complex Numbers and the Complex Exponential 1. Complex numbers The equation x2 + 1 = 0 has no solutions, because for any real number xthe square x 2is nonnegative, and so x + 1 can never be less than 1. In spite of this it turns out to be very useful to assume that there is a number ifor which one has (1) i2 = −1. Any complex number is then an expression of the form a+ bi, where aand bare old Introduction: Exponential form of complex numbers makes use of the mathematical constant e and the property. which is also called Euler's Formula. A complex number is normally defined in its Cartesian form as an expression of the form. where x and y are real numbers i is defined as the imagined square root of -1, i.e. i satisfies the condition Polar form : z = [ cos( ) + i sin ] Exponential form: z = e i More References and links Operations on Complex Numbers in Polar Form Complex Numbers - Basic Operations Questions on Complex Numbers Maths Calculators and Solver 2. The exponential form of a complex number Using the polar form, a complex number with modulus r and argument θ may be written z = r(cosθ +j sinθ) It follows immediately from Euler's relations that we can also write this complex number in exponential form as z = rejθ. Exponential form z = rejθ When using this form you should ensure that all angles are measured in radians and not degrees

This complex exponential function is sometimes denoted cis x ( c osine plus i s ine). The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula. Euler's formula is ubiquitous in mathematics, physics, and engineering In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol called the imaginary unit, and satisfying the equation i2 = −1. Because no real number satisfies this equation, i was called an imaginary number by René Descartes Written in exponential form, the complex numbers z 1 and z 2 are: $\begin{split} z_{1}&=2.24 \cdot e^{i \cdot 0.4636}\\ z_{2}&=2.24 \cdot e^{i \cdot 1.1071} \end{split}$ Moivre's formula for power of complex numbers. If we need to compute the power of a complex number, z n, where n is a natural number, we can use Moivre's formula

Exponent of Complex Numbers » Play with the forms of the complex number → component form a + ib a + i b → polar form r(cosθ + isinθ) r (cos θ + i sin θ Let z 1 = r 1 exp. ⁡. ( i θ 1) and z 2 = r 2 exp. ⁡. ( i θ 2) be complex numbers in exponential form and z = z 1 + z 2 , then I know using the complex plane vector representation that z can be written in the exponential form too, z = r exp. ⁡. ( i θ) , where. r = r 1 2 + r 2 2 + 2 r 1 r 2 cos. ⁡ to denote a complex number: z = reiθ, called the exponential form. Key Point 9 The exponential form of a complex number is z = reiθ in which r = |z| and θ = arg(z) so z = reiθ = r(cosθ +i sinθ) 22 HELM (2008): Workbook 10: Complex Numbers With Euler's formula we can rewrite the polar form of a complex number into its exponential form as follows. z =reiθ z = r e i θ where θ = argz θ = arg z and so we can see that, much like the polar form, there are an infinite number of possible exponential forms for a given complex number convert complex numbers between exponential and Cartesian (algebraic/rectangular) forms, convert complex numbers between exponential form and polar form, perform operations (addition, subtraction, multiplication, and division) on complex numbers in exponential form, use the properties of complex numbers in exponential form to solve problems

Complex numbers expand the scope of the exponential function, It turns out that there is always a solution of (1) of the form x = ert, for an appropriate constant r. To see what r should be, take x = ert for an as yet to be determined constant r, substitute it into (1), and apply the Exponential Principle. We ﬁnd (r 2 + cr + k)e rt = 0. Cancel the exponential (which, conveniently, can. The exponential form is simply an alternative way of expressing a complex number This is why the complex unit circle can be seen as being exponential. Furthermore, if two complex numbers on the unit circle are multiplied, the resulting number is located at the sum of the circumference scale values of the two numbers on the unit circle. z1 ⋅z2 = ip1 ⋅ ip2 = i(p1+p2) = z3 z 1 ⋅ z 2 = i p 1 ⋅ i p 2 = i ( p 1 + p 2) = z 3 Put ������ equals five root three ������ to the ������ over three ������ in algebraic form. We've been given this complex number ������ in exponential form. That's the form ������ equals ������������ to the ������������, where ������ is the absolute value of the complex number and ������ is its argument measured in radians

I saw this and this question after googling which made me wonder about whether the exponential form of complex numbers would still work. $z = a\begin{pmatrix} 1&0\\ 0&1 \end{pmatrix}+b\begin{pmatrix} 0&1\\ -1&0 \end{pmatrix} = \begin{pmatrix} a&b\\ -b&a \end{pmatrix} = Me^P$   Addition: I just found this article which I dont really understand, but where they solve a case similar to. Example questions of complex numbers in exponential formGo to http://www.examsolutions.net to see the index, playlists and more maths videos on complex numbe.. Commented: Star Strider on 25 Mar 2015. This is the question I have and I have no idea how to write the code! Convert the complex number 8-7j into exponential and polar form. [2 marks] I know already. syms a a=8-7j [theta, r]cart2pol (8, 7) for the polar for but thats it

The modulus of a complex number , also called the complex norm, is denoted and defined by. If is expressed as a complex exponential (i.e., a phasor ), then. The complex modulus is implemented in the Wolfram Language as Abs [ z ], or as Norm [ z ]. The square of is sometimes called the absolute square . Let and be two complex numbers Using exponential form to find complex rootsWatch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_number_chal.. Convert the complex number 8-7j into exponential and polar form. [2 marks

### 15.2 - Complex Numbers in Polar and Exponential For

1. The absolute value or modulus is the distance of the image of a complex number from the origin in the plane. The calculator uses the Pythagorean theorem to find this distance. Very simple, see examples: |3+4i| = 5 |1-i| = 1.4142136 |6i| = 6 abs(2+5i) = 5.3851648 Square root Square root of complex number (a+bi) is z, if z 2 = (a+bi). Here ends simplicity. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. If you want to find out.
2. If you have a complex number z = r (cos (θ) + i sin (θ)) written in polar form, you can use Euler's formula to write it even more concisely in exponential form: z 5. Exponential Form of Complex Number. (Mar 09, 2021) Polar form. r (cos θ + j sin θ) = r cis θ = r∠θ. θ can be in.
3. Convert Complex Numbers to Polar Form. Added Dec 6, 2015 by Squarerootofpi in Mathematics. ----. Send feedback | Visit Wolfram|Alpha
4. Convert a complex number from the exponential form to its algebraic form. Graphic representation z is a complex number represented by the point M on the plane of complex numbers as follows, Polar and exponential form The polar and exponential forms of z are written, z = r *( cos(\varphi) + i * sin(\varphi)) = r * e^(i*\varphi) r = |z| is the modulus from z. \varphi is the argument from z.
5. ator to polar form. sin β + i cos β = cos (90 - β) + i sin (90 - β) Then, (cos α + i sin α) 3 / (sin β + i cos β) 4 = (cos α + i sin α) 3 / [cos (90 - β) + i sin (90 - β)] 4. Convert the above complex numbers to exponential form. cos α + i sin α = e i4 �
6. We see that in some circumstances the exponential form is even more convenient than the polar form since we need not worry about cumbersome trigonometric relations. HELM (2006): Section 10.3: The Exponential Form of a Complex Number. 23. Tas k Express the following complex numbers in exponential form: (a)z= 1−i (b)z= 2 + 3i (c)z=− 6

### To Exponential Form Of Complex Numbers Online Math Homewor

Our number forms of complex exponential form, used quite important to. Theorem that these examples to convert complex number in the plane is very useful in polar coordinate plane. How do string form to numbers which could not complex numbers are defined function always done to solve a complex numberrepresent a loading icon on your help. They will be in exponential form or imaginary number in. Exponential form of complex numbers: Exercise Transform the complex numbers into Cartesian form: 6-1 Precalculus a) z= 2e i π 6 b) z= 2√3e i π 3 c) z= 4e3πi d) z= 4e i π 2 e) z= √2e i 3π 4 f) z= 2√3e i 2π 3 g) z= √3e i 13π Subject: Exponential form Name: Austin Who are you: Student. When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is -1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks. Hi Austin, To express -1 + i in the form r e i = r (cos() + i sin()) I. ### Convert a Complex Number to Polar and Exponential Forms

• The complex exponential. We don't yet have a deﬁnition of eit. Let's hope that we can deﬁne it so that the Exponential Principle holds. This means that it should be the solution of the initial value problem z˙ = iz, z(0) = 1 . We will probably have to allow it to be a complex valued function, in view of the i in the equation. In fact, I can produce such a function: z = cos t + i sin t.
• It's good for multiplication because the product, so here's any number in its polar form. That's a general complex number. It's modulus times e to the i theta times r two e to the i theta two--Well, you just multiply them as ordinary numbers. So, the part out front will be r1 r2, and the e to the i theta parts gets multiplied by the exponential law and becomes e to the i (theta one plus theta.
• (The Presentations actually includes a polar form for a complex number of modulus r and argument theta that displays in the form r \[Angle] theta. And ComplexToPolar yields that form. Hence the need for the outside function PolarToExp. Thus there is a distinction made between polar form and exponential form -- as there should be.) Share. Improve this answer. Follow edited Jun 20 '15 at 9.

### Euler's formula - Wikipedi

Apart from Rectangular form (a + ib ) or Polar form ( A ∠±θ ) representation of complex numbers, there is another way to represent the complex numbers that is Exponential form. This is similar to that of polar form representation which involves in representing the complex number by its magnitude and phase angle, but with base of exponential function e, where e = 2.718 281 Two formulas for calculating root of a complex number in a exponential form. Last Post; Oct 14, 2010; Replies 1 Views 1K. Help with finding the modulus, polar form and polar exponential form. Last Post; Apr 24, 2012; Replies 2 Views 3K. Converting standard to polar form. Last Post; Apr 14, 2017; Replies 6 Views 946. Converting to Polar and Cartesian form. Last Post; Oct 17, 2014; Replies 4. Trigonometry and Complex Exponentials Amazingly, trig functions can also be expressed back in terms of the complex exponential. Then everything involving trig functions can be transformed into something involving the exponential function. This is very surprising. In order to easily obtain trig identities like , let's write and as complex. The following figure shows the complex number z = 2 + 4j Polar and exponential form. As you can see from the figure above, the point A could also be represented by the length of the arrow, r (also called the absolute value, magnitude, or amplitude), and its angle (or phase), φ relative in a counterclockwise direction to the positive horizontal axis. This is the polar form of a complex number

Need your ASSIGNMENT done? Use our paper writing service to score better and meet your deadline. Order a Similar Paper HERE Order a Different Paper HERE Write each complex number in exponential form (Complex Exponential Form) 10 September 2020. Complex Numbers Complex numbers consist of real and imaginary parts. You may already be familiar with complex numbers written in their rectangular form: a0 +b0j where j = √ −1. Here, a0 is called the real part and b0 is called the imaginary part. We will often represent these numbers using a 2-d space we'll call the complex plane. For example. Convert the complex number 8-7j into exponential and polar form. [2 marks] I know already. syms a a=8-7j [theta, r]cart2pol(8, 7) for the polar for but thats it. Find all five values of the following expression, giving your answers in Cartesian form: (-2+5j)^(1/5) [6 marks] Any ideas? 0 Comments. Show Hide -1 older comments. Sign in to comment. Sign in to answer this question. Answers (1) Star. How to convert this complex number to exponential form? [closed] Ask Question Asked 2 years, 7 months ago. Active 2 years, 7 months ago. Viewed 402 times -1 $\begingroup$ Closed. This question is off-topic. It is not currently accepting answers.. Exponential Form of a Complex Number, Euler Formula. April 3, 2013. by pankajchauhan2013. YouTube. kamlesh kumar Rangra. 27 subscribers. Subscribe. Exponential Form of a Complex Number, Euler Formula. Watch later

View Notes - Complex Numbers - Exponential Form from ELECTRICAL BSEE/039J at Technical University of Mombasa. The Exponential Form of a Complex Number 10.3 Introduction In this Section we introduc Question: convert complex number to exponential form. Posted: digerdiga 340 Product: Maple 2018. + Add Tags. 0. How do I convert a complex number to abs and arg presentation. For example: z=1+1*I would be z=sqrt (2)*exp (I*Pi/4) or when doing a calculation how can I tell him to always present these number in that form and do not expand out. Thanks The complex set can be seen as a plane where each number can be defined by coordinates (algebraic form) or a distance and angle (exponential form). Complex numbers have the property to be solutions of some equations that cannot be solved by usual real numbers, such as the equation x 2 =-1

The complex exponential polar form of a complex number is most convenient when calculating a complex multiplication or division. (see Appendix A) Complex Exponential Signals The complex exponential signal is defined as It's a complex-valued function of t, where the magnitude of z(t) is | z(t)|= A and the angle of z(t) is Using Euler's formula 3 DSP, CSIE, CCU The real part is a real cosine. CARTESIAN FORM EXPONENTIAL FORM POLAR FORM FORM OF COMPLEX NUMBER TRIGONOMETRIC FORM BNSA/JMSK 9. CARTESIAN FORM z = a + bi Example : i) -5 + 3i ii) 4 + 6i iii) -7 - 7i BNSA/JMSK 10. POLAR FORM z = Modulus = R Arg Argument Example : i) 4.5 45° ii) 6 123.6° iii) 7.8 330° BNSA/JMSK 11  ### Complex number - Wikipedi

our complex number as: rej Complex exponential form simpli es expression of delay property. delay complex exponential form trig form T/2 T/4 t0. Fourier Series Matching Match the signals (left column) to Fourier series coe cients (right). t x1(t) 0 11=4 1 k Re XA [k] k Im A t x2(t) 0 11=4 1 k Re XB [k] k Im B t x3(t) 0 11=4 1 k Re XC [k] k Im C t x4(t) 1=4 1 k Re XD [k] k Im D. Title: MIT. Exponential and polar forms of a complex number. Allowed: constants, operators and i. For the product, use* Ex: a*b and not ab. Do you have any suggestions to improve this page ? This tool converts a complex number from the algebraic format (a + b.i) to its exponential and polar forms

Figure 5.2.1: Trigonometric form of a complex number. To find θ, we have to consider cases. If z = 0 = 0 + 0i ,then r = 0 and θ can have any real value. If z ≠ 0 and a ≠ 0, then tan(θ) = b a. Determine the polar form of the complex numbers w = 4 + 4√3i and z = 1 − i. 1 This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i 2 = −1 or j 2 = −1.The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar coordinates (magnitude and angle) The complex exponential function, viewed geometrically. Create Class; Home. News Feed. Resources. Profile Drag the blue points to see the effect of adding the complex number a to various shapes. The checkboxes show different shapes. The before shape is filled in, and is traced by the blue point P. The after shape is not filled, and is traced by P'. This applet shows the function f(z)=e. this still outputs an answer in complex number form, what i need from matlab is my answer to be outputted in the exponential form i.e (8-7i) would be converted to '10.6e^-.7i' if at all possibl Details. A complex number can be visually represented using a two-dimensional Cartesian coordinate system as an ordered pair of real numbers on the complex plane. The representation of a complex number in terms of its Cartesian coordinates in the form , where is the imaginary unit, is called the algebraic form of that complex number. The coordinate is called the real part and the imaginary.

Exponential Form of a Complex Number. Subject: Mathematics. Age range: 17 - 18. Resource type: Other (no rating) 0 reviews. Teach Further Maths. 4.75 47 reviews 'Teach Further Maths' is a suite of Maths PowerPoint presentations for Teachers and Students of Further Mathematics A Level, AS Level or equivalent. 68 high quality, fully animated colour further maths PowerPoint presentations. Complex Sinusoids. Recall Euler's Identity , Multiplying this equation by and setting , where is time in seconds, is radian frequency, and is a phase offset, we obtain what we call the complex sinusoid : Thus, a complex sinusoid consists of an in-phase'' component for its real part, and a  phase-quadrature '' component for its imaginary part This online calculator will help you to convert rectangular form of complex number to polar and exponential form. Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to convert rectangular form of complex number to polar and exponential form The polar form of a complex number is a different way to represent a complex number apart from rectangular form. Usually, we represent the complex numbers, in the form of z = x+iy where 'i' the imaginary number. But in polar form, the complex numbers are represented as the combination of modulus and argument. The modulus of a complex number is also called absolute value. This polar form is.

### Complex numbers representation - x-engineer

Polar form of a complex number, modulus of a complex number, exponential form of a complex number, argument of comp and principal value of a argument. Math Preparation point All defintions of mathematics. e.g 9th math, 10th math, 1st year Math, 2nd year math, Bsc math(A course+B course), Msc math, Real Analysis, Complex Analysis, Calculus, Differential Equations, Algebra, Group Theory. Roots of Complex Numbers; Example 1; Example 2 Cube Roots of Unity; In a complex number, a+ib, a is the real part and b is the imaginary part, although, of course, both a and b are real numbers. The complex conjugate of z=a+ib is z*=a-ib. You can express complex numbers in various forms, including algebraic, trigonometric and exponential form. Home / Complex Number Primer. Notes. Next Section . Show Mobile Notice Show All Notes Hide All Notes. Mobile Notice. You appear to be on a device with a narrow screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your. Click here������to get an answer to your question ️ Express the following complex number in polar form and exponential form : - 1 - √(3)

Feb 20, 2018 - This video explains how to write a complex number given in Cartesian form in exponential form Write the complex number $360^{\circ}$ in exponential form. MathsGee Q&A Bank, Africa's largest personalized FREE Study Help network that helps people find answers to problems and connect with experts for improved outcomes Complex exponential functions† A complex number is an expression of the form z = a + ib, where a and b are real numbers and i is the symbol that is introduced to serve as a square root of −1. The real part of z = a + ib is the real number a, and the imaginary part of z = a + ib is the real number b. Real numbers are considered to be complex numbers with zero imaginary parts. a + ib is the. The polar form of complex numbers emphasizes their graphical attributes: (the distance of the number from the origin in the complex plane) and (the angle that the number forms with the positive Real axis). These are also called and . Created with Raphaël Not only can we convert complex numbers that are in exponential form easily into polar form such as: 2e = 2∠30, 10e = 10∠120 or -6e = -6∠90, but Euler's identity also gives us a way of converting a complex number from its exponential form into its rectangular form. Then the relationship between, Exponential, Polar and Rectangular form in de ning a complex number is given as. Complex.

Exponential form, polar form, Cartesian form for... Learn more about complex numbers, exponential form, polar form, cartesian form, homework MATLA Complex number to polar form. Follow 423 views (last 30 days) Show older comments. Tobias Ottsen on 20 Oct 2020. Vote. 0. ⋮ . Vote. 0. Commented: Rik on 28 Apr 2021 Hi . How do i calculate this complex number to polar form? z = (10<-50)*(-7+j10) / -12*e^-j45*(8-j12) 0 Comments. Show Hide -1 older comments. Sign in to comment. Sign in to answer this question. Answers (3) Ameer Hamza on 20 Oct. The calculator will find the polar form of the given complex number, with steps shown. Complex number: If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below. Your Input. Find the polar form of $$\sqrt{3} + i$$$. Solution. The standard form of the complex number is $$\sqrt{3} + i$$$. For a complex. Figure 1: (a) Several points in the complex plane. (b) The polar form of a complex number. Clearly jzjis a non-negative real number, and jzj= 0 if and only if z = 0. Note that jzj= jzj, i.e., a complex number and its complex conjugate have the same magnitude

### Complex Numbers : Exponent and Root of Complex Number

Division of Complex Numbers (8:54) WORKSHEET SECTION 2: ROOTS AND COMPLEX NUMBERS Square Root of a Complex Number (9:00). 1. Identify the modulus and argument of the complex number. In this case, we have: $$r=4\sqrt{2}, \ \theta=\frac{3\pi}{2}$$ *Note: Since the argument is already in radians, we can just substitute it into the exponential form formula (shown in next step).However, if it was in degrees, we would have to first convert it into radians (recall how to do that here) before substituting Exponential form of a complex number Thread starter blues1; Start date Oct 16, 2010; Oct 16, 2010 #1 blues1. 2 0. Homework Statement if z = -2 + 2i find r and θ The Attempt at a Solution our teacher told us that when we have z = a + bi r = sqrt(a^2 + b^2) and θ = tan^-1(b/a) so here it's supposed to be r = sqrt(8) and θ = - pi/4 but using wolfram alpha to see if the results are matching I.

### Sum of complex numbers in exponential form formula

Synonyme (Andere Wörter) für Complex number exponential form & Antonyme (Entgegengesetzte Bedeutung) für Complex number exponential form Polar form of complex number: The real part of a complex exponential function can be used to represent an AC voltage or current. The impedance can then be expressed as a complex exponential. Impedance combinations: Phasor diagrams: The impedance of the individual circuit elements can then be expressed as pure real or imaginary numbers. RL and. Complex number form converter. This calculator allows one to convert complex number from one representation form to another with step by step solution. For example, you can convert complex number from algebraic to trigonometric representation form or from exponential back to algebraic, ect. To use the calculator, one need to choose. Synonyms for Complex Number Exponential Shape (other words and phrases for Complex Number Exponential Shape). Log in. Synonyms for Complex number exponential shape. 18 other terms for complex number exponential shape- words and phrases with similar meaning. Lists. synonyms. antonyms. definitions. examples. thesaurus. words. phrases. Parts of speech. nouns. Tags. base. exponent. form. complex. (iv) While finding the solution of equation of form x 2 + 1 = 0, x 2 + x + 1 = 0, the set of real number was extended into set of complex numbers. First of all 'Euler' represented $$\sqrt{-1}$$ by the symbol i and proved that the roots of every algebraic equation are number of the form a + ib where a, b ∈ R. A number of this form called complex Number  Sinónimos (Otras palabras) para Complex number exponential form & Antónimos (Significado opuesto) para Complex number exponential form Complex Numbers Exponential Form. Thread starter helloeveryone; Start date Apr 28, 2017; Search Forums; New Posts; H. Thread Starter. helloeveryone. Joined Apr 8, 2011 64. Apr 28, 2017 #1 I would appreciate some help with the following problem: Last edited by a moderator: Apr 28, 2017. Like Reply. Scroll to continue with content. MrAl. Joined Jun 17, 2014 8,174. Apr 28, 2017 #2 Hi, Just one. View Notes - Exponential Form of a Complex Number from ECET 110 at DeVry University, Arlington. Exponential Form of a Complex Number IMPORTANT: In this section, MUST be expressed in radians. We us Exponential Form of a Complex Number (A-Level Further Maths) 'Teach Further Maths' is a suite of Maths PowerPoint presentations for Teachers and Students of Further Mathematics A Level, AS Level or equivalent. 68 high quality, fully animated colour further maths PowerPoint presentations, consisting of over 3000 slides - a comprehensive teaching. Write each complex number in exponential form.  Ernest C. Numerade Educator. Like. Report. Jump To Question Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26.

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