Question

please help meee
Express(2+I)^-2 in the form of (a+ib)​

Answer 1

Answer:

${(2 + i)}^{ - 2}$

$= \frac{1}{ {(2 + i)}^{2} }$

$= \frac{1}{4 + ( - 1) + 2 \times 2 \times i}$

$= \frac{1}{3 + 4i}$

$= \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i}$

$= \frac{3 - 4i}{ {(3)}^{2} - {(4i)}^{2} }$

$= \frac{3 - 4i}{9 - ( - 16)}$

$= \frac{3 - 4i}{9 + 16}$

$= \frac{3 - 4i}{25}$

$= \frac{3}{25} - \frac{4}{25} i$