What is (a+bi)/(c+di) ?

The solution to (a+bi)/(c+di) is (ac+bd)/(c^2+d^2)+(-ad+bc)/(c^2+d^2)i

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simplify (a+bi)/(c+di)

simplify

\frac{a + bi}{c + d i}

\frac{a c + b d}{c ^{2} + d ^{2}} + \frac{- a d + b c}{c ^{2} + d ^{2}} i

Solution steps

\frac{a + bi}{c + d i}

Multiply by the conjugate

\frac{c - d i}{c - d i}

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

Simplify

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

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

Rewrite in standard complex form:

\frac{a c + b d}{c ^{2} + d ^{2}} + \frac{- a d + b c}{c ^{2} + d ^{2}} i

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

3 \frac{1}{6} - 1 \frac{1}{2} + \frac{1}{3}

(3 x + 2) (2 x - 4)

\frac{7}{14}

\frac{1}{4} \cdot \frac{1}{6}

2 (- \frac{3}{11}) - 2 (\frac{27}{22})

What is (a+bi)/(c+di) ?
The solution to (a+bi)/(c+di) is (ac+bd)/(c^2+d^2)+(-ad+bc)/(c^2+d^2)i