What is (2/3+12i}{-7+\frac{1i)/4} ?

The solution to (2/3+12i}{-7+\frac{1i)/4} is -16/471-808/471 i

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simplify (2/3+12i}{-7+\frac{1i)/4}

simplify

\frac{\frac{2}{3} + 12 i}{- 7 + \frac{1 i}{4}}

- \frac{16}{471} - \frac{808}{471} i

Solution steps

\frac{\frac{2}{3} + 12 i}{- 7 + \frac{1 i}{4}}

Rewrite

- 7 + \frac{1 i}{4}

in standard complex form:

- 7 + \frac{1}{4} i

= \frac{\frac{2}{3} + 12 i}{- 7 + \frac{1}{4} i}

Multiply by the conjugate

\frac{- 7 - \frac{1}{4} i}{- 7 - \frac{1}{4} i}

= \frac{( \frac{2}{3} + 12 i ) ( - 7 - \frac{1}{4} i )}{( - 7 + \frac{1}{4} i ) ( - 7 - \frac{1}{4} i )}

Simplify

\frac{( \frac{2}{3} + 12 i ) ( - 7 - \frac{1}{4} i )}{( - 7 + \frac{1}{4} i ) ( - 7 - \frac{1}{4} i )} : \frac{- \frac{5}{3} - \frac{505}{6} i}{\frac{785}{16}}

= \frac{- \frac{5}{3} - \frac{505}{6} i}{\frac{785}{16}}

Apply the fraction rule:

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

= \frac{- \frac{5}{3}}{\frac{785}{16}} + \frac{- \frac{505}{6}}{\frac{785}{16}} i

Simplify

\frac{- \frac{5}{3}}{\frac{785}{16}} + \frac{- \frac{505}{6}}{\frac{785}{16}} i : - \frac{16}{471} - \frac{808}{471} i

= - \frac{16}{471} - \frac{808}{471} i

\frac{0. 5 ^{10}}{0. 5 ^{7}}

- 1 - 11

36 m^{2} n - 9 mn + 12 m n^{2}

\frac{5}{20} - \frac{3}{14} + \frac{2}{7}

8 \times (- 6)

What is (2/3+12i}{-7+\frac{1i)/4} ?
The solution to (2/3+12i}{-7+\frac{1i)/4} is -16/471-808/471 i