Question

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

Answer 1

Rationalise the denominator to find:

`(2+3i)/(1+2i)=8/5-1/5i`

Explanation:

Multiply both numerator and denominator by the Complex conjugate `1-2i` of the denominator as follows:

`(2+3i)/(1+2i)=((2+3i)(1-2i))/((1+2i)(1-2i))`

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

`=(8-i)/5`

`=8/5-1/5i`