Could someone show me how to solve these two problems-I have 10 of each kind to do this weekend and I'm really lost

Question

1. Find product of 8(cos pi/2 + i sin pi/2) * 1/2(cos pi/6 + i sin pi/6)

2. Same problem but find quotient instead of product
Please someone show me these two so I can do my other problems from these examples
Thankyou Thank you

Answer 1

1. That can be written
8*e^(i*pi/2) * (1/2)e^(i pi/6)
= 4 e^(2i*pi/3)
= 4 [cos(2*pi/3) + i sin (2*pi/3)]
= -2 + 2(sqrt3)i

2. The quotient is
16 e^(i*pi/3)
= 16[cos(pi/3) + i sin(pi/3)]
= 8 + 8 sqrt3 i

Answer 2

Thank you very much for showing me the steps but they don't match my answers that are available: Could you possibly further explain-I'm messed up right now on this concept-
the answers for Number 1 are
4cis(2pi/3)
4cis(pi/3)
4cis(pi/8)
4cis(pi/4)
2. answers for number two are:
16cis(pi/3)16cis(2pi/3)
4cis(2pi/3)
4cis(pi/3)

Answer 3

cis Theta = cos Theta + i sin Theta

x = r cos Theta
y = r sin Theta

so for example
4 cis 2 pi/3 = 4 cos 2 pi/3 + 4 i sin 2pi/3
but cos 2p/i/3 = -.5 and sin 2pi/3 = sqrt 3/2
so
x = 4 (-.5) = -2
y = 4 (.5/ sqrt 3) = 2 sqrt3
-2 + 2 i sqrt 3
Your answer is the same as that of WLS