Explanation Formula used: Polar form : For any point ( x , y ) in the complex plane, the equations relating x , y , r and θ are, x = r cos θ y = r sin θ r 2 = x 2 + y 2 tan θ = y x where, the length r is the absolute value and θ is the argument of the complex number. The rectangular form x + y j of a complex number can be converted to the polar form as x + y j = r ( cos θ + j sin θ ) by using the above equations. Calculation: The given number and complex number are 21 and 3 − 9 j . Compute the polar form of the number 21 as follows. Compare the number 21 with the general form of the complex number x + y j . Here, x = 21 and y = 0 . Obtain the value of r as follows. Substitute x = 21 and y = 0 in r 2 = x 2 + y 2 . r 2 = 21 2 + 0 2 r = 21 2 + 0 2 r = 21 That is, the value of r is 21. Obtain the angle θ as follows. Substitute x = 21 and y = 0 in tan θ = y x . tan θ = 0 21 θ ref = tan − 1 ( 0 21 ) θ ref = 0 ° That is, the angle θ ref is 0 ° To determine To perform: The indicated operation in the expression ( 21 ) ( 3 − 9 j ) and express the result in rectangular and polar form. To determine To check: The answer by performing the indicated operation on ( 21 ) ( 3 − 9 j ) in rectangular form.

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Question

Chapter 12.6, Problem 29E

To determine

To change: The number 21 and complex number 3−9j into polar form.

To determine

To perform: The indicated operation in the expression (21)(3−9j) and express the result in rectangular and polar form.

To determine

To check: The answer by performing the indicated operation on (21)(3−9j) in rectangular form.

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Chapter 12.6, Problem 28E

Chapter 12.6, Problem 30E

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