Question

Find the number of integral solution of $(1-i{)}^x=2^x$.

Answer 1

Let first find the value of $|1-i|$

$1-i$ is the complex no in the form of $x+iy=0$

where $x=1$ and $y=-1$

$|1-i|=\sqrt{2}$

Given $|1-i{|}^x=2^x$

$\Rightarrow (\sqrt{2}{)}^x=2^x$

$\Rightarrow (\sqrt{2}{)}^x=(\sqrt{2}{)}^{2x}$

compair power

$\Rightarrow x=2x$

$\Rightarrow x=0$

So the answer is $0$

Hence, there is only $1$ integral solution.