z = 1 + 7i( 2 i)^2 = 1 + 7i4 1 4i = 1 + 7i3 4i×3 + 4i3 + 4i = ( 3 + 4i) ×( 1 + 7i)9 + 16 = 3 + 21i + 4i 2825 = 25 + 25i25 = ...

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Algebra of Complex Numbers

Simplify 1+...

Question

Simplify $\frac{1 + 7 i}{(2 - i)^{2}}$

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Solution

$z = \frac{1 + 7 i}{{(2 - i)}^{2}} = \frac{1 + 7 i}{4 - 1 - 4 i} = \frac{1 + 7 i}{3 - 4 i} \times \frac{3 + 4 i}{3 + 4 i}$

$= \frac{(3 + 4 i) \times (1 + 7 i)}{9 + 16}$

$= \frac{3 + 21 i + 4 i - 28}{25}$

$= \frac{- 25 + 25 i}{25}$

$= - 1 + i$

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