Question

Simplify the given expression below: 2 divided by the quantity of 2 plus 5i

Answer 1

Remove the imaginary from the denominator.
$\frac{2}{2 + 5i}$
$( \frac{2}{2 + 5i} )( \frac{2 - 5i}{2 - 5i} )$
$\frac{2(2 - 5i)}{(2 + 5i)(2 - 5i)}$
$\frac{4 - 10i}{4 - 10i + 10i - 25 i^{2} }$  $i^{2} = -1$
$\frac{4 - 10i}{4 + 25}$
$\frac{4 - 10i}{29}$