How do you simplify $\frac{4 + 9 i}{2 + 6 i}$ $(4+9i)/(2+6i)$ ?

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Answer 1 · 2018-04-05T15:19:30

$\frac{31 - 3 i}{20}$ $frac{31 - 3i}{20)$

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

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

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

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

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

$\frac{62 - 6 i}{40} =$ $frac{62 - 6i}{40) =$

Reduce to lowest terms:

$\frac{31 - 3 i}{20}$ $frac{31 - 3i}{20)$

How do you simplify (4+9i)/(2+6i)4+9i2+6i(4+9i)/(2+6i)?