COMPLEX NUMBERS AND DEMOIVRE'S THEOREM: HELP ASAP

a = 0, b = -15

Step-by-step explanation:

Given two complex number Z1=3cispi and z2=5cis(pi/2)

In polar form;

z1 = 3(cospi + isinpi)

z1 = 3(-1+i0)

z1 = -3+0i

Z2 =  5(cospi/2 + isinpi/2)

Z2 = 5(0+i)

Z2 = 0+5i

Z1*Z2 =  (-3+0i)(0+5i)

Z1*Z2 = 0 - 15i +0i + 0i²

Z1*Z2 = 0-15i

comparing 0-15i with a + bi;

a = 0 and b = -15

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)