Determine the following...

Question

Given: a= -cis (π/6) and b= 1/2cis (-π/3)

Determine:

1. ab
2. a/b
3. a²
4. b⁶

Answer 1

-cos(pi/6) = -cos(30) = -sqrt(3)/2

(1/2)cos(-pi/3) = (1/2)(cos(-60)) = (1/2)(cos(300)) = (1/2)(1/2) = 1/4

(1) -sqrt(3)/8

(2) -sqrt(3)/2 * 4 = -2*sqrt(3)

(3) 3/4

(4) 1/1536