Question

I am having difficulty with two problems:

1) Evaluate (1+i)^12 by using DeMoivre's Theorem. Express the result in rectangular form.
So far I have: r=sqrt(1)^2+(1)^2 which simplified is sqrt2. Don't know how to proceed.

2) Write the polar equation theta = 45 degrees in rectangular form.
I don't even know how to proceed to do this.

Any help would be great!

Answer 1

(1+i)^12 is sqrt2 @ 45 to the 12th power, or sqrt2 ^12 @45x12

1@45 is .707i + .707j where i,j are unit vectors in the x,y directions.

Answer 2

x = r cos(45) ...(1)
y = r sin(45) ...(2)

Dividing (2) by (1):
y / x = tan(45) = 1
y = x.

Answer 3

find the distance between points at (6,-3) and (-1,4). The answer I got was 9.9 and it was wrong.
please help!