Question

Help please! :)
w= -2-2i
calculate w^4 and express answer in polar form.

Answer 1

Well, let's get it into polar form first. Do you remember how to get r?

Answer 2

r^2=x^2+y^2 right?

Answer 3

so r would equal sqrt8 @Psymon

Answer 4

Right, which reduces to 2sqrt(2).Now we just need theta by saying tan(theta) = b/a. So b = -2 and a = -2. So now we need to say that tan(theta) = 1. SO what angle of theta makes tan(theta) = 1?

Answer 5

is it pi/4?

Answer 6

That is one value. But look at your rectangular form. You're in quadrant 3. You see why?

Answer 7

5pi/4 because it's (cosine, sine) is (-sqrt2/2,-sqrt2/2) and the answer was 2sqrt2

Answer 8

Right, so the angle is 5pi/4. SO your polar form is:
\[2\sqrt{2}(\cos \frac{ 5\pi }{ 4 }+ isin \frac{ 5\pi }{ 4 })\]So now when we need to raise this polar form to a power, this is the formula:
\[r ^{n}(\cos(n \theta) + isin(n \theta))\]Where n is the power we want. So basically, take your r to the 4th power and multiply your angles by 4 :3

Answer 9

thanks so much! :)

Answer 10

Mhm ^_^