I am not sure about this because I cannot do the very last bit of trigonometry but this is what I have got so far:

Using a right angled triangle in the Argand diagram:

Use the rule of multiplying by the complex conjugate pair:

Using standard trigonometric results we need this in terms of cot(A/2):

I have put in the minus sign in now. Well spotted anonimnystefy.

k = 0 is not a solution I agree Stefy, but why does my answer not work for k = 0 ?

EDIT: I now can see that cot(0) is not possible. Given that cot X = 1/(tan X) if X=0 then we have a division by zero.

Therefore the argument is not valid for this case.