Question

$$\frac{S=-1+1^{5}}{2+i}+\frac{8+19i^{2},P=$$

Evaluate

$\left(-\frac{4}{5}+\frac{2}{5}i\right)rt_{1}^{5}+\left(\frac{2}{5}-\frac{1}{5}i\right)s_{2}+\left(\frac{3}{40}+\frac{2}{5}i\right)$

Expand

$\left(-\frac{4}{5}+\frac{2}{5}i\right)rt_{1}^{5}+\left(\frac{2}{5}-\frac{1}{5}i\right)s_{2}+\left(\frac{3}{40}+\frac{2}{5}i\right)$