Solve Modulus for (3-4i)^10/(2-i)^8

[hadroneater]

Homework Statement

Find the modulus for:
(3 - 4i)^10/(2 - i)^8

Homework Equations

The Attempt at a Solution

I tried putting the two terms in their exponential forms. Then do simple exponential operations and convert back to cartesian form to get the modulus.
3 - 4i = 5e^{arctan(-4/3)}
2 - i = \sqrt{5}e^{arctan(1/2)}

However the arguments aren't going to be exact numbers. Is there another way to approach this question?

 

[Dick]

Homework Statement

Find the modulus for:
(3 - 4i)^10/(2 - i)^8

Homework Equations

The Attempt at a Solution

I tried putting the two terms in their exponential forms. Then do simple exponential operations and convert back to cartesian form to get the modulus.
3 - 4i = 5e^{arctan(-4/3)}
2 - i = \sqrt{5}e^{arctan(1/2)}

However the arguments aren't going to be exact numbers. Is there another way to approach this question?

You left out an i on your exponents in polar form. But that's besides the point. Don't you think modulus of 3-4i would just be 5? Why or why not?

 

[hadroneater]

Right. I confused the definition of Modulus with Conjugate. Man, I feel stupid.

Thanks!