# Math Help - Complex Loci Question

1. ## Complex Loci Question

Hi, could some please explain the process for the following:

Given arg((z+2)/(z-2i)) = pi/4, show -2i lies in the locus

Is it a case of converting to cartesian or is it something far simpler such as subbing in?

Thanks

2. We have

$\dfrac{-2i+2}{-2i-2i}=\ldots=\dfrac{1}{2}+\dfrac{1}{2}i$

so,

$\arg \left(\dfrac{1}{2}+\dfrac{1}{2}i\right)=\dfrac{\pi}{4}$

3. Brilliant and makes absolute sense

4. Originally Posted by robertbrooks
Brilliant

I don't agree.

and makes absolute sense
I agree.