What is ((3-4i)^3)/(2+i) ?

The solution to ((3-4i)^3)/(2+i) is -278/5+29/5 i

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simplify ((3-4i)^3)/(2+i)

simplify

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

- \frac{278}{5} + \frac{29}{5} i

Solution steps

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

Multiply by the conjugate

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

= \frac{( 3 - 4 i ) ^{3} ( 2 - i )}{( 2 + i ) ( 2 - i )}

Simplify

\frac{( 3 - 4 i ) ^{3} ( 2 - i )}{( 2 + i ) ( 2 - i )} : \frac{29 i - 278}{5}

= \frac{29 i - 278}{5}

Rewrite in standard complex form:

- \frac{278}{5} + \frac{29}{5} i

= - \frac{278}{5} + \frac{29}{5} i

- 9 x^{3} 54 + 4 x^{2} 96 x^{2}

3 x^{1} \cdot 2 x^{2}

(\frac{x}{4} - \frac{1}{x})^{2}

\frac{2}{1 + 5}

\frac{39 x ^{3} y}{26 x ^{2} y ^{2}}