How do you simplify #(4+9i)/(2+6i)#?

1 Answer
Apr 5, 2018

Answer:

#frac{31 - 3i}{20)#

Explanation:

Start by multiplying both the numerator and the denominator by the conjugate of the denominator:

#(frac{4 + 9i}{2 + 6i})(frac{2 - 6i}{2 - 6i}) =#

Use the distributive property to get back to a single fraction:

#frac{8 - 6i - 54i^{2}}{4 - 36i^{2}) =#

Convert #i^{2}# to #-1# and combine like terms:

#frac{62 - 6i}{40) =#

Reduce to lowest terms:

#frac{31 - 3i}{20)#