Question

How do you simplify `2/(5-2i)`?

Answer 1

the simplified form is `10/29+(4i)/29`

Explanation:

To simplify, multiply the numerator and denominator by the conjugate of the denominator `5+2i`

so `z=2/(5+2i)=(2(5+2i))/((5-2i)(5+2i))=(10+4i)/(25-4i^2)`

`i^2=-1`

So `z=(10+4i)/29=10/29+(4i)/29`