What is (i^{87})/(-2+3i) ?

The solution to (i^{87})/(-2+3i) is -3/13+2/13 i

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simplify (i^{87})/(-2+3i)

simplify

\frac{i ^{87}}{- 2 + 3 i}

- \frac{3}{13} + \frac{2}{13} i

Solution steps

\frac{i ^{87}}{- 2 + 3 i}

Multiply by the conjugate

\frac{- 2 - 3 i}{- 2 - 3 i}

= \frac{i ^{87} ( - 2 - 3 i )}{( - 2 + 3 i ) ( - 2 - 3 i )}

Simplify

\frac{i ^{87} ( - 2 - 3 i )}{( - 2 + 3 i ) ( - 2 - 3 i )} : \frac{2 i - 3}{13}

= \frac{2 i - 3}{13}

Rewrite in standard complex form:

- \frac{3}{13} + \frac{2}{13} i

= - \frac{3}{13} + \frac{2}{13} i

- 18 + 7

- 990 - 160

(\frac{5 x ^{- 2}}{6 y ^{- 2}})^{- 3}

\frac{48}{5 + 13}

4 - 2 3^{2} - 16