Question

How do you simplify `(1+2i)/(2-3i)`?

Answer 1

`(1+2i)/(2-3i)=(-4+7i)/13=-4/13+7/13i`

Explanation:

1. Find the complex coniugate of denominator

denominator: `z=2-3i`

denominator complex coniugate: `bar(z)=2color(red)+3i`

1. Multiply both numerator and denominator for the complex coniugate

`(1+2i)/(2-3i)*(2+3i)/(2+3i)=(2+3i+4i+6i^2)/(2^2-(3i)^2)=`

Remembering that: `i^2=-1`

`=(2+6*(-1)+7i)/(4-9i^2)=(2-6+7i)/(4-9*(-1))=(-4+7i)/(4+9)=`
`=(-4+7i)/13=-4/13+7/13i`