What is (5-6i)/(-5+10i) ?

The solution to (5-6i)/(-5+10i) is -17/25-4/25 i

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simplify (5-6i)/(-5+10i)

simplify

\frac{5 - 6 i}{- 5 + 10 i}

- \frac{17}{25} - \frac{4}{25} i

Solution steps

\frac{5 - 6 i}{- 5 + 10 i}

Multiply by the conjugate

\frac{- 5 - 10 i}{- 5 - 10 i}

= \frac{( 5 - 6 i ) ( - 5 - 10 i )}{( - 5 + 10 i ) ( - 5 - 10 i )}

Simplify

\frac{( 5 - 6 i ) ( - 5 - 10 i )}{( - 5 + 10 i ) ( - 5 - 10 i )} : \frac{- 85 - 20 i}{125}

= \frac{- 85 - 20 i}{125}

Apply the fraction rule:

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

= \frac{- 85}{125} + \frac{- 20}{125} i

Simplify

\frac{- 85}{125} + \frac{- 20}{125} i : - \frac{17}{25} - \frac{4}{25} i

= - \frac{17}{25} - \frac{4}{25} i

sec^{2} (x) cot (x) sin^{2} (x)

820

(\frac{- 1 + i 3}{2})^{2}

1.6 \cdot 1 0^{5}

1.6 \cdot 1 0^{6}