What is (4+5i)/(2+6i) ?

The solution to (4+5i)/(2+6i) is 19/20-7/20 i

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simplify (4+5i)/(2+6i)

simplify

\frac{4 + 5 i}{2 + 6 i}

\frac{19}{20} - \frac{7}{20} i

Solution steps

\frac{4 + 5 i}{2 + 6 i}

Multiply by the conjugate

\frac{2 - 6 i}{2 - 6 i}

= \frac{( 4 + 5 i ) ( 2 - 6 i )}{( 2 + 6 i ) ( 2 - 6 i )}

Simplify

\frac{( 4 + 5 i ) ( 2 - 6 i )}{( 2 + 6 i ) ( 2 - 6 i )} : \frac{38 - 14 i}{40}

= \frac{38 - 14 i}{40}

Apply the fraction rule:

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

= \frac{38}{40} + \frac{- 14}{40} i

Simplify

\frac{38}{40} + \frac{- 14}{40} i : \frac{19}{20} - \frac{7}{20} i

= \frac{19}{20} - \frac{7}{20} i

(4 x) (x)

100 \cdot \frac{3}{5}

\frac{4}{4}