Question

• (1/5+i2/5) - (4+i5/2)

Answer 1

The expression given to us is

$$\begin{gathered} \left(\frac{1}{5}+\frac{i^2}{5}\right)-\left(\frac{4}{}+\frac{i^5}{2}\right) \\ =\left(\frac{1}{5}+\frac{i^2}{5}\right)-\left(4+\frac{i^5}{2}\right),(i^2=-1) \\ =\left(\frac{1}{5}+\frac{(-1)}{5}\right)-\left(4+\frac{{\left(i^2\right)}^2\times i}{2}\right) \\ =\left(\frac{1}{5}-\frac{1}{5}\right)-\left(4+\frac{{\left(-1\right)}^2\times i}{2}\right) \\ =0-\left(4+\frac{1\times i}{2}\right) \\ =-\left(4+\frac{i}{2}\right),\mathrm{where}i=\sqrt{-1} \end{gathered}$$


Hence, the answer.