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 complex number is − 1 − j . Compute the polar form of the complex number − 1 − j as follows. Compare the complex number − 1 − j with the general form of the complex number x + y j . Here, x = − 1 and y = − 1 . Obtain the value of r as follows. Substitute x = − 1 and y = − 1 in r 2 = x 2 + y 2 To determine To perform: The indicated operation in the expression ( − 1 − j ) 3 ; Express the result in rectangular and polar form. To determine To check: The answer by performing the indicated operation on ( − 1 − j ) 3 in rectangular form.

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Question

Chapter 12.6, Problem 34E

To determine

To change: The complex number −1−j into polar form.

To determine

To perform: The indicated operation in the expression (−1−j)3; Express the result in rectangular and polar form.

To determine

To check: The answer by performing the indicated operation on (−1−j)3 in rectangular form.

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Chapter 12.6, Problem 33E

Chapter 12.6, Problem 35E

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