Calculating angle between two complex numbers

[polaris90]

so I have z1 = 3 + j, z2 = -5 + 5j, z3 = z1+z2 = -2 + 6j

the question is, show that angle(z1) and angle(z1 + z2) differ by an integer multiple of pi/2.

I tried doing it this way
arctan(z1/z3), but then I always end up with a number that doesn't work. I know that arctan(x) cannot equal pi/2. Is there another way t rewrite it? I computed it using MATLAB and it gave me pi/2.

 

[LCKurtz]

Just draw the corresponding vectors $\langle 3,1\rangle$ and $\langle -1,3\rangle$ and look at their dot product.

 

[Filip Larsen]

Perhaps you can utilize that pi/2 means the two complex numbers, when viewed as vectors in the complex plane, must be perpendicular to each other.