How do you simplify #(1-2i)/(3-4i)#? Precalculus Complex Numbers in Trigonometric Form Complex Number Plane 1 Answer Richard 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# Answer link Related questions What is the complex number plane? Which vectors define the complex number plane? What is the modulus of a complex number? How do I graph the complex number #3+4i# in the complex plane? How do I graph the complex number #2-3i# in the complex plane? How do I graph the complex number #-4+2i# in the complex plane? How do I graph the number 3 in the complex number plane? How do I graph the number #4i# in the complex number plane? How do I use graphing in the complex plane to add #2+4i# and #5+3i#? How do I use graphing in the complex plane to subtract #3+4i# from #-2+2i#? See all questions in Complex Number Plane Impact of this question 2895 views around the world You can reuse this answer Creative Commons License