(1/5+i2/5) - (4+i5/2)

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Solution

The expression given to us is

$(\frac{1}{5} + \frac{i^{2}}{5}) - (\frac{4}{} + \frac{i^{5}}{2}) = (\frac{1}{5} + \frac{i^{2}}{5}) - (4 + \frac{i^{5}}{2}), (i^{2} = - 1) = (\frac{1}{5} + \frac{(- 1)}{5}) - (4 + \frac{{(i^{2})}^{2} \times i}{2}) = (\frac{1}{5} - \frac{1}{5}) - (4 + \frac{{(- 1)}^{2} \times i}{2}) = 0 - (4 + \frac{1 \times i}{2}) = - (4 + \frac{i}{2}), where i = \sqrt{- 1}$

Hence, the answer.

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