Question

Express the given complex number ${\left(\frac{2-3i}{1+i}\right)}^5$in the form of a+ib.

Answer 1

Given,

${\left(\frac{2-3i}{1+i}\right)}^5$

${(\frac{2-3i}{1+i}\times \frac{1-i}{1-i})}^5$

$={\left(\frac{-1-5i}{2}\right)}^5$

$=\frac{-2876-1900i}{32}$

$=\frac{-719-475i}{8}$

$=-\frac{719}{8}-i\frac{475}{8}$