Question:
Express the given complex number in the form $a+i b:\left(\frac{1}{5}+i \frac{2}{5}\right)-\left(4+i \frac{5}{2}\right)$
Solution:
$\left(\frac{1}{5}+i \frac{2}{5}\right)-\left(4+i \frac{5}{2}\right)$
$=\frac{1}{5}+\frac{2}{5} i-4-\frac{5}{2} i$
$=\left(\frac{1}{5}-4\right)+i\left(\frac{2}{5}-\frac{5}{2}\right)$
$=\frac{-19}{5}+i\left(\frac{-21}{10}\right)$
$=\frac{-19}{5}-\frac{21}{10} i$