Question

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

Answer 1

Multiply by 1, written as the complex conjugate of the bottom of the fraction divided by itself, in this case `(1-2i)/(1-2i)`:

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

Explanation:

Multiply top and bottom of the fraction by the complex conjugate of the bottom. For a complex expression `a+bi` the complex conjugate is `a-bi`.

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

While simplifying, remember `i^2=-1`

`= (2-i+6)/(1+4)=(8-i)/5`