Complex Numbers: Euler's formula problem

[WWCY]

Homework Statement

Homework Equations

The Attempt at a Solution

I attempted to use the formula z_j = x_j + iy_j to substitute both z's. Further simplification gave me (x₁ + x₂)cosθ + (y₂ - y₁)sinθ or, Re(z₂ + z₁)cosθ + Im(z₂ - z₁)sinθ.

Is this a valid answer? Or are there any other identities I should have used to obtain an answer purely in 'z'?

I don't seem to be able to reduce the problem into Acosθ + Bcosθ any other way.

Thanks in advance!

 

[haruspex]

Re(z2 + z1)cosθ + Im(z2 - z1)sinθ.

Looks good to me.

 

[WWCY]

Looks good to me.

Thank you!