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

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Answer 1 · 2018-04-05T15:19:30

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

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)#