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

1 Answer
Jan 12, 2016

(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