What is (19+7i)/(4-5i) ?

The solution to (19+7i)/(4-5i) is 1+3i

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simplify (19+7i)/(4-5i)

simplify

\frac{19 + 7 i}{4 - 5 i}

1 + 3 i

Solution steps

\frac{19 + 7 i}{4 - 5 i}

Multiply by the conjugate

\frac{4 + 5 i}{4 + 5 i}

= \frac{( 19 + 7 i ) ( 4 + 5 i )}{( 4 - 5 i ) ( 4 + 5 i )}

Simplify

\frac{( 19 + 7 i ) ( 4 + 5 i )}{( 4 - 5 i ) ( 4 + 5 i )} : \frac{41 + 123 i}{41}

= \frac{41 + 123 i}{41}

Apply the fraction rule:

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

= \frac{41}{41} + \frac{123}{41} i

Simplify

\frac{41}{41} + \frac{123}{41} i : 1 + 3 i

= 1 + 3 i

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