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Express each of these complex numbers in polar form and in exponential form: a. Za = 5 – j5; b. Zz = -10 + j5; c. Z, = -3 - j4; d. Za = -j12.

Express each of these complex numbers in polar form and in exponential form: a. Za = 5 – j5; b. Zz = -10 + j5; c. Z, = -3 - j4; d. Za = -j12.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Complex Numbers in Polar and Exponential Form** The task is to express each of the following complex numbers in both polar form and exponential form: **a.** \( Z_a = 5 - j5 \) **b.** \( Z_b = -10 + j5 \) **c.** \( Z_c = -3 - j4 \) **d.** \( Z_d = -j12 \) Complex numbers can be represented in polar form as \( r(\cos \theta + j\sin \theta) \) and in exponential form as \( re^{j\theta} \), where \( r \) is the magnitude and \( \theta \) is the phase angle.
Transcribed Image Text:**Complex Numbers in Polar and Exponential Form** The task is to express each of the following complex numbers in both polar form and exponential form: **a.** \( Z_a = 5 - j5 \) **b.** \( Z_b = -10 + j5 \) **c.** \( Z_c = -3 - j4 \) **d.** \( Z_d = -j12 \) Complex numbers can be represented in polar form as \( r(\cos \theta + j\sin \theta) \) and in exponential form as \( re^{j\theta} \), where \( r \) is the magnitude and \( \theta \) is the phase angle.
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