Complex Numbers Equation with Real Solutions

[atarr3]

Homework Statement

Find real numbers p and q such that the following equation is true:

$$\frac{p}{q+5i}=4e^{\frac{-i\pi}{4}}$$

Homework Equations

Euler's formula

The Attempt at a Solution

Ok so I converted the right side to rectangular form using Euler's formula and solved for p. But I don't really know what do after that.

I got $$p=5\sqrt{2}q+25\sqrt{2}+25i\sqrt{2}-5qi\sqrt{2}$$ but I don't know how to simplify this any further.

 

[atarr3]

Maybe $$p$$ is equal to the real part of the right side and the imaginary part must equal zero. Which would make $$q=5$$ and $$p=50\sqrt{2}$$?

 

[diazona]

Maybe $$p$$ is equal to the real part of the right side and the imaginary part must equal zero. Which would make $$q=5$$ and $$p=50\sqrt{2}$$?

Yep, that'll do it.

 

[atarr3]

Haha ok thank you. I guess I didn't need to post this after all.