**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.

a Za=5-j5 ΩZa=52∠-45° ΩZa=52e-jπ4 Ω b Za=-10+j5 ΩZa=11.18∠-26.56° ΩZa=52e-jπ6.77 Ω

Answered: Express each of these complex numbers…

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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental frequency and harmonics) through a process called Fourier analysis.

Question

**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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