Question

Complex numbers zj and zz are given by zj = 3- j2, zz = - 4 + j3. (a) express zj and zz in polar form. (b) find lz1l by first applying eq. (1.41) and then by applying eq. (1.43). (c) determine the product zj zz in polar form

Answer 1

Solution:

Given: zj = 3- j2, zz = - 4 + j3

Part a:

zj = 3- j2 = $3.6e^{-j33.7^{\circ}}$

zz = - 4 + j3 = $5e^{j143.1^{\circ}}$

Part b:

|zj| = |3− j2| =  √3² +(−2)² = √13 = 3.60

|z1| =  √(3− j2)(3+ j2) = √ 13 = 3.60.

Part c:

With the help of part a:

z1z2 = $3.6e^{-j33.7^{\circ}}.5e^{j143.1^{\circ}}$