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

1 Answer
Mar 9, 2018

(-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