What is factor (-1-9i)/(-2-9i) ?

The solution to factor (-1-9i)/(-2-9i) is 83/85+i 9/85

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factor (-1-9i)/(-2-9i)

factor

\frac{- 1 - 9 i}{- 2 - 9 i}

\frac{83}{85} + i \frac{9}{85}

Solution steps

\frac{- 1 - 9 i}{- 2 - 9 i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = - 1, b = - 9, c = - 2, d = - 9

= \frac{( - 1 \cdot ( - 2 ) + ( - 9 ) ( - 9 ) ) + ( - 9 ( - 2 ) - ( - 1 ) ( - 9 ) ) i}{( - 2 ) ^{2} + ( - 9 ) ^{2}}

Refine

= \frac{83 + 9 i}{85}

Rewrite

\frac{83 + 9 i}{85}

in standard complex form:

\frac{83}{85} + \frac{9}{85} i

= \frac{83}{85} + \frac{9}{85} i

- 23 + 2 i

- \infty - \infty + \infty

7 (6^{2} - 2 \cdot 6 + 91)

5 x + 15 x

m^{(2)} + 3 m + 9

What is factor (-1-9i)/(-2-9i) ?
The solution to factor (-1-9i)/(-2-9i) is 83/85+i 9/85