simplify (4i)/(2-i)

Solution

simplify

\frac{4 i}{2 - i}

- \frac{4}{5} + \frac{8}{5} i

Solution steps

\frac{4 i}{2 - i}

Multiply by the conjugate

\frac{2 + i}{2 + i}

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

Simplify

\frac{4 i ( 2 + i )}{( 2 - i ) ( 2 + i )} : \frac{8 i - 4}{5}

= \frac{8 i - 4}{5}

Rewrite in standard complex form:

- \frac{4}{5} + \frac{8}{5} i

= - \frac{4}{5} + \frac{8}{5} i

\frac{x ^{2}}{1 - x ^{2}}

- 36 + - 25

\frac{3 x - 1}{x ^{2}} + \frac{x - 9}{3 x}

\frac{2}{7} - \frac{1}{8}

3 (- 0.3 k + 2 k + 9) - 5 k