Question

Express the given complex number in the form $a+ib:$$(\frac{1}{5}+i\frac{2}{5})-(4+i\frac{5}{2})$

Answer 1

$(\frac{1}{5}+i\frac{2}{5})-(4+i\frac{5}{2})$
$=\frac{1}{5}+\frac{2}{5}i-4-\frac{5}{2}i$
$=(\frac{1}{5}-4)+i(\frac{2}{5}-\frac{5}{2})$
$=\frac{-19}{5}+i\left(\frac{-21}{10}\right)$
$=\frac{-19}{5}-\frac{21}{10}i$
$=a+ib,$ where $a=-\frac{19}{5},b=-\frac{21}{10}$