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Popular >

simplify (41)/(5+4i)

Solution

simplify

\frac{41}{5 + 4 i}

Solution

5 - 4 i

Solution steps

\frac{41}{5 + 4 i}

Multiply by the conjugate

\frac{5 - 4 i}{5 - 4 i}

= \frac{41 ( 5 - 4 i )}{( 5 + 4 i ) ( 5 - 4 i )}

Simplify

\frac{41 ( 5 - 4 i )}{( 5 + 4 i ) ( 5 - 4 i )} : \frac{205 - 164 i}{41}

= \frac{205 - 164 i}{41}

Apply the fraction rule:

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

= \frac{205}{41} + \frac{- 164}{41} i

Simplify

\frac{205}{41} + \frac{- 164}{41} i : 5 - 4 i

= 5 - 4 i

Popular Examples

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\frac{x ^{2}}{x + 1} \geq - 1

(x + 2) (x - 2) = 0

Frequently Asked Questions (FAQ)

What is (41)/(5+4i) ?
The solution to (41)/(5+4i) is 5-4i