What is (1+7i)/(9+9i) ?

The solution to (1+7i)/(9+9i) is 4/9+1/3 i

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simplify (1+7i)/(9+9i)

simplify

\frac{1 + 7 i}{9 + 9 i}

\frac{4}{9} + \frac{1}{3} i

Solution steps

\frac{1 + 7 i}{9 + 9 i}

Multiply by the conjugate

\frac{9 - 9 i}{9 - 9 i}

= \frac{( 1 + 7 i ) ( 9 - 9 i )}{( 9 + 9 i ) ( 9 - 9 i )}

Simplify

\frac{( 1 + 7 i ) ( 9 - 9 i )}{( 9 + 9 i ) ( 9 - 9 i )} : \frac{72 + 54 i}{162}

= \frac{72 + 54 i}{162}

Apply the fraction rule:

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

= \frac{72}{162} + \frac{54}{162} i

Simplify

\frac{72}{162} + \frac{54}{162} i : \frac{4}{9} + \frac{1}{3} i

= \frac{4}{9} + \frac{1}{3} i

p^{3} q^{3} - p^{2} q^{2} - pq + 1

36 \cdot \frac{5}{18}

x^{6} - 10 x^{4} y^{2} + 9 x^{2} y^{4}

\frac{1}{2} + \frac{5}{3}

(x^{2} + 8)^{2} - 8