Question

How do you simplify `(-3 + 2i) / (2 - 5i)`?

Answer 1

`(-3+2i)/(2-5i)=-16/29-11/29i`

Explanation:

To simplify `(-3+2i)/(2-5i)`, we need to multiply numerator and denominator by complex conjugate of the denominator i.e. here `2+5i`.

Hence, `(-3+2i)/(2-5i)=((-3+2i)(2+5i))/((2-5i)(2+5i))`

= `(-6-15i+4i+10i^2)/(4-25i^2)`

= `(-6-15i+4i-10)/(4+25)`

= `(-16-11i)/29=-16/29-11/29i`