Question

if z=a-ai and (2z+3)^2012=(z+5)^2012
find a

Answer 1

The trick is to write everything in polar form. For example,
z = a.sqrt(2).exp(-pi.i/4)

Do the same for 2z + 3 and z + 5. And then these seemingly impossible exponents will become a lot easier to deal with.

Answer 2

thanks