- #1

Bng1290

- 5

- 0

## Homework Statement

I'm pretty sure that I just don't fully understand these problems so I think I just need help getting pushed in the right direction here. Anyways, here's the problem I'm on.

Evaluate and give your answer in Cartesian Coordinates:

[tex]\left|(1-3i)^5(\sqrt{2}+i\sqrt{3})^7\right|[/tex]

## Homework Equations

[tex]\left|z\right|[/tex]= r = sqrt(x^2+y^2)

z=x+iy=re^(i[tex]\Theta[/tex])

z^n=r^n e^(in[tex]\Theta[/tex])

## The Attempt at a Solution

I've tried to convert to polar form (re^i[tex]\Theta[/tex]) and raising r to the nth power and multiplying the angle by n for each of the two separate complex numbers and then multiplying together from there. Then I assume I would have to convert back to cartesian coords for the answer. I honestly think I'm missing something important with all of this as I thought that the absolute value of a complex number was its modulus and thus I would not be able to get any answer that could be presented in cartesian coordinates. I've read through my book on this subject and can't really figure out what to do, which is what I meant when I said I need help getting in the right direction.