Question

How do you simplify `(1-2i)/(3-4i)`?

Answer 1

`(-2i+11)/25`

Explanation:

Multiply by the conjugate of `(3+4i)/(3+4i)` to cancel out the imaginary numbers in the denominator. Also remember that `i^2` is equal to -1.

`=(1-2i)/(3-4i) * (3+4i)/(3+4i)`
`=(3+4i-6i-8i^2)/(9+12i-12i-16i^2)`
`=(-2i+3-8(-1))/(9-16(-1))`
`=(-2i+11)/25`