simplify 8/(2+6i)

Solution

simplify

\frac{8}{2 + 6 i}

\frac{2}{5} - \frac{6}{5} i

Solution steps

\frac{8}{2 + 6 i}

Multiply by the conjugate

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

= \frac{8 ( 2 - 6 i )}{( 2 + 6 i ) ( 2 - 6 i )}

Simplify

\frac{8 ( 2 - 6 i )}{( 2 + 6 i ) ( 2 - 6 i )} : \frac{16 - 48 i}{40}

= \frac{16 - 48 i}{40}

Apply the fraction rule:

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

= \frac{16}{40} + \frac{- 48}{40} i

Simplify

\frac{16}{40} + \frac{- 48}{40} i : \frac{2}{5} - \frac{6}{5} i

= \frac{2}{5} - \frac{6}{5} i

6 4^{- \frac{4}{3}}

2 (x + 10)^{2} - 34 = - 26

7 r^{2} - 5 = 2 r + 9 r^{2}

(\frac{1}{h ^{- 2}})^{- 1} \cdot h^{3}

\frac{3}{2} + 8