Question

Simplify and express the result in the form of $a+bi$:
$-i(9+6i)(2-i{)}^{-1}$

Answer 1

$\frac{-i(9+6i)}{2-i}$ $\Rightarrow \frac{-9i-6i^2}{2-i}$ $\Rightarrow \frac{6-9i}{2-i}$

Multiplying and dividing by $2+i$

$\frac{6-9i}{2-i}\times \frac{2+i}{2+i}$

$\Rightarrow \frac{(6-9i)(2+i)}{(2{)}^2-(i{)}^2}$

$\Rightarrow \frac{12+6i-18i-9i^2}{4+1}$

$\Rightarrow \frac{12+9-12i}{5}$

Thus the $a+bi$ form is $\frac{21}{5}-\frac{12}{5}i$ or $4.2-2.4i$