# Solution to $(1-i)^n =2^n$ [closed]

Okay. Find the integral solution of $$(1-i)^n =2^n$$

I just want to know who's to do this which is explained in as many steps as possible. Thanks in advance.

• It's not possible to give an explanation in as many steps as possible, sorry. Given an explanation, there exists another explanation with more steps. – David C. Ullrich Oct 6 '15 at 14:08
• @David C. Ullrich: Is that an Incompleteness theorem for explanations ? – Bernard Oct 6 '15 at 14:13
• Okay. Just explain to me the basic idea as to how I can solve this question. – Giridhar Oct 6 '15 at 14:14
• @Bernard Why, I suppose it is. I'm gonna be famous. Godel, Church, Turing, Ullrich... cool. – David C. Ullrich Oct 6 '15 at 14:21
• @Giridhar Hint: Write $1+i$ in the form $re^{i\theta}$. – David C. Ullrich Oct 6 '15 at 14:21

\begin{align} |(1-i)^n| &= |2^n|\\ |1-i|^n &= |2|^n\\ (\sqrt2)^n &= 2^n \end{align}
The only potential solution is $n=0$