Question

Solve (z+i)^4=z^4

Answer 1

i is the imaginary unit, z belongs to the complex number system

Answer 2

I haven't seen an example quite like this in class and cannot figure it out myself. I have tried expanding and using z=a+bi and didn't get anywhere.

Answer 3

It's is basically a cubic in z.
\((z+i)^4-z^4=0\)
On expansion and simplification,
\((z+i)^4-z^4=4iz^3-6z^2+4iz+1=0\)

Answer 4

I might have misled you. I am able to find the roots using the above expansion.
But when I come to think of it, I did not have the reflex of thinking about de Moivre's theorem. Perhaps it is more intuitive looking at the given form of the problem.