What is ((1+3i))/((1+i)) ?

The solution to ((1+3i))/((1+i)) is 2+i

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simplify ((1+3i))/((1+i))

simplify

\frac{( 1 + 3 i )}{( 1 + i )}

2 + i

Solution steps

\frac{1 + 3 i}{1 + i}

Multiply by the conjugate

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

= \frac{( 1 + 3 i ) ( 1 - i )}{( 1 + i ) ( 1 - i )}

Simplify

\frac{( 1 + 3 i ) ( 1 - i )}{( 1 + i ) ( 1 - i )} : \frac{4 + 2 i}{2}

= \frac{4 + 2 i}{2}

Apply the fraction rule:

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

= \frac{4}{2} + \frac{2}{2} i

Simplify

\frac{4}{2} + \frac{2}{2} i : 2 + i

= 2 + i

\frac{9}{4} \cdot 2

\frac{36}{121}

18 x^{3} + 29 x^{2} + 3 x

(a b^{- 1} + b a^{- 1}) (a^{- 2} + b^{- 2})^{- 1}

\frac{2 y}{3} + \frac{2 y}{5} < \frac{16 y}{15} - \frac{1}{3}