finding polar and cartesian form for this power

charmedbeauty

1. The problem statement, all variables and given/known data

((-1+i)/(√2))^1002
find polar and cartesian form

2. Relevant equations



3. The attempt at a solution


So I started by finding |z|=1

and Arg(z)= arctan (-1) = 5pi/6

so 1^(1002)*e^(i*5pi/6)*1002 =1*e^(i*835pi)

but thats as far as I got because the answer says -i, but to get that term I need 1*e^-ipi/2

any thoughts??

HallsofIvy

Your main problem is that [itex]arctan(-1)[/itex] is NOT [itex]5\pi/6[/itex]!

Calculate that again.

charmedbeauty

I was assuming since the original eqn has a negative real part then I would add Pi/2 since the angle is measured from 0.
Although Im getting 3pi/4 now

NewtonianAlch

Well, yes (3pi)/4 is the angle you're looking for since this is in the second quadrant.

You have got |z|, and now you have the angle.

Put it into exponential form to the power of 1002, and simplify it to get the angle in terms of a principal argument.

charmedbeauty

Ok so now I have 1^1002*(cos 3Pi/4+isin3Pi/4)

= 1*(0)=0 how do they get the minus i?

NewtonianAlch

How did you get 0 for (cos 3Pi/4 + isin 3Pi/4) ?

Also, you have forgotten to raise that to the power.

charmedbeauty

isnt cos 3pi/4=-0.7...

and sin 3pi/4=0.7...

NewtonianAlch

Yes, but you have a complex number there.

-0.707 +0.707i

You can't add them just like that.

What of the 1002? You need to account for that too.