In class we showed that any complex number Z can be written in either of the following two forms:Z = X+jYZ = |Z| ejTo go between these two forms, you can use the following relationships:|Z| = √X² +Y²YXX = |Z| cos oY = |Z| sinoWe also introduced one more quantity called the complex conjugate of Z, which is denoted Z*. Tofind the complex conjugate of Z, you simply reverse the sign in front of all the j's. So, for example,if:Z = X+jY= |Z| e¹then:tan o =Z* = X-jY= |Z| e-jThe complex conjugate is useful because it can be used to calculate |Z|, the magnitude of Z.Consider, for example, the following product:ZZ* = (x+jY) (X -jY) = x² + y² = |Z|².Alternatively, using the exponential form of Z:ZZ = (|Z|e¹) (|Z| e-jº) = |Z|².In both cases we get that ZZ* = |Z|². 1. Consider the complex number:(1)(a) Any complex number can be written in the form Z = X+jY or Z = |Z|ejo. Find X and Yfor the complex number given in Eq. (1).(b) Find the complex conjugate Z*.12-3jZ=(d) What is the value of o in degrees?(c) Find |Z and tan for this complex number.

Answered: Image /qna-images/answer/f50dc3db-9291-4e55-9cf7-76f84c328d3b.jpg

1. Consider the complex number: 1 2-3j Z (1) (a) Any complex number can be written in the form Z = X + JY or Z = |Z|e. Find X and Y for the complex number given in Eq. (1). (b) Find the complex conjugate Z*. (c) Find [Z] and tan o for this complex number. (d) What is the value of in degrees?

1. Consider the complex number: 1 2-3j Z (1) (a) Any complex number can be written in the form Z = X + JY or Z = |Z|e. Find X and Y for the complex number given in Eq. (1). (b) Find the complex conjugate Z*. (c) Find [Z] and tan o for this complex number. (d) What is the value of in degrees?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

PLEASE HELP
A digital signal is defined as x[n] = cos(n4π/5) Is this a digital sequence periodic? Find the first eight elements in the sequence.
Please full answer and draw y(t) for each period . The y-axis for both is 1
Find the Power of the following discrete time signal x[n] = 2e^j3n Please give detailed steps
1-In your own words and no more than three lines, explain the main difference(s) between Gauss's law and other integral-differential equations. 2-In your own words and no more tham two hnes, explan the main difference(s) between Coulomb's law and other laws.
Task & exciress Convert the following continuous signals into discrete * signals if f =1o000Hz. i. F(t)=5 sin(100*pi*t) ii. F(t)=2 cos(1000*pi*t) iii. F(t)=4 sin(8o0*pi*t)
The CTFT of x(t)= 5 rect((t+4)/6) is: Select one: a. 30 sinc(6f) e-j8 pi t b. 30 sinc(6f) e-j8 pi f c. 30 sinc(6f) ej8 pi f d. 30 sinc(6f) ej48 pi f
1-)Examine the graphs of the DSB (t) and VSB (t) signals in the time space. What are the differences?2-)How many sine waves does the resulting VSB signal contain? What are the frequencies of these signals?
Q23 answer required only
Given: A 2a,- 4.3a, + a, and B = a, + 2a, - 3a,. Find the z-component of (2A + B) x (A-2B). a. 35.00 b. 76.93 OC. -54.50 d. 41.50 Your answer is incorrect. The correct answer is: 41.50
Matlab Question Skaler Variables Make the following variable: D) z= e?ns, where j is the imaginary number and e is Euler's number (use exp, pi)
A 60microHenry inductance is connected across a given supply voltage. Find the La Place transform of its voltage.