Posted by **Tammie** on Saturday, October 8, 2011 at 9:04pm.

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

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

- Pre-Calc -
**drwls**, Saturday, October 8, 2011 at 9:27pm
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

- Pre-Calc-Pleas recehck -
**Tammie**, Saturday, October 8, 2011 at 9:38pm
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)

- Pre-Calc -
**Damon**, Sunday, October 9, 2011 at 9:33am
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

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