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: It is given that, the complex numbers are 5 j − 2 and − 1 − j . Compute the polar form of the complex number 5 j − 2 as follows. Compare the complex number 5 j − 2 with the general form of the complex number x + y j . Here, x = − 2 and y = 5 . Obtain the value of r as follows. Substitute x = − 2 and y = 5 in r 2 = x 2 + y 2 . r 2 = ( − 2 ) 2 + 5 2 r = ( − 2 ) 2 + 5 2 r = 4 + 25 r = 5.38 That is, the value of r is 5.38. Obtain the angle θ as follows. Substitute x = − 2 and y = 5 in tan θ = y x . tan θ = 5 − 2 θ ref = tan − 1 ( − 5 2 ) θ ref = − 68.19 ° θ ref = − 68.2 ° [ Round to nearest ones ] That is, the angle θ ref is − 68.2 ° . The angle θ ref is in the second quadrant as the real part of 5 j − 2 is negative and the imaginary part is positive To determine To perform: The indicated operation in the expression ( 5 j − 2 ) ( − 1 − j ) ; Express the result in rectangular and polar form.

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Question

Chapter 12.6, Problem 26E

To determine

To change: The complex numbers 5j−2 and −1−j into polar form.

To determine

To perform: The indicated operation in the expression (5j−2)(−1−j); Express the result in rectangular and polar form.

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Chapter 12.6, Problem 25E

Chapter 12.6, Problem 27E

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