What is (4-3i)/(6-4i) ?

The solution to (4-3i)/(6-4i) is 9/13-1/26 i

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simplify (4-3i)/(6-4i)

simplify

\frac{4 - 3 i}{6 - 4 i}

\frac{9}{13} - \frac{1}{26} i

Solution steps

\frac{4 - 3 i}{6 - 4 i}

Multiply by the conjugate

\frac{6 + 4 i}{6 + 4 i}

= \frac{( 4 - 3 i ) ( 6 + 4 i )}{( 6 - 4 i ) ( 6 + 4 i )}

Simplify

\frac{( 4 - 3 i ) ( 6 + 4 i )}{( 6 - 4 i ) ( 6 + 4 i )} : \frac{36 - 2 i}{52}

= \frac{36 - 2 i}{52}

Apply the fraction rule:

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

= \frac{36}{52} + \frac{- 2}{52} i

Simplify

\frac{36}{52} + \frac{- 2}{52} i : \frac{9}{13} - \frac{1}{26} i

= \frac{9}{13} - \frac{1}{26} i

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