# Express the given complex number in the form a + ib:

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:

$\left(\frac{1}{5}+i \frac{2}{5}\right)-\left(4+i \frac{5}{2}\right)$

$=\frac{1}{5}+\frac{2}{5} i-4-\frac{5}{2} i$

$=\left(\frac{1}{5}-4\right)+i\left(\frac{2}{5}-\frac{5}{2}\right)$

$=\frac{-19}{5}+i\left(\frac{-21}{10}\right)$

$=\frac{-19}{5}-\frac{21}{10} i$