What is (6+2i)/(1+2i) ?

The solution to (6+2i)/(1+2i) is 2-2i

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simplify (6+2i)/(1+2i)

simplify

\frac{6 + 2 i}{1 + 2 i}

2 - 2 i

Solution steps

\frac{6 + 2 i}{1 + 2 i}

Multiply by the conjugate

\frac{1 - 2 i}{1 - 2 i}

= \frac{( 6 + 2 i ) ( 1 - 2 i )}{( 1 + 2 i ) ( 1 - 2 i )}

Simplify

\frac{( 6 + 2 i ) ( 1 - 2 i )}{( 1 + 2 i ) ( 1 - 2 i )} : \frac{10 - 10 i}{5}

= \frac{10 - 10 i}{5}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{10}{5} + \frac{- 10}{5} i

Simplify

\frac{10}{5} + \frac{- 10}{5} i : 2 - 2 i

= 2 - 2 i

- 48 \div 8

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