Question

How do you divide `(-4+10i)/(3+4i)`?

Answer 1

`(-4+10i)/(3+4i)=28/25+46/25 i`

Explanation:

To divide `-4+10i` by `3+4i`, one should multiply numerator and denominator by complex conjugate of denominator `3+4i` i.e. `3-4i`. Also remember that `i^2=-1`.

`(-4+10i)/(3+4i)`

= `((-4+10i)×(3-4i))/((3+4i)×(3-4i))`

= `(-4)×3+(-4)(-4i)+10i×3+10i×((-4i))/(3×3+3×(-4i)+4i×3+4i×(-4i))`

= `(-12+16i+30i-40i^2)/(9-12i+12i-16i^2)`

= `(-12+46i-40×(-1))/(9-16×(-1))`

= `(-12+46i+40)/(9+16)`

= `(28+46i)/25`

= `28/25+46/25 i`