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Popular >

simplify 1/(4+5i)

Solution

simplify

\frac{1}{4 + 5 i}

Solution

\frac{4}{41} - \frac{5}{41} i

Solution steps

\frac{1}{4 + 5 i}

Multiply by the conjugate

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

= \frac{1 \cdot ( 4 - 5 i )}{( 4 + 5 i ) ( 4 - 5 i )}

Simplify

\frac{1 \cdot ( 4 - 5 i )}{( 4 + 5 i ) ( 4 - 5 i )} : \frac{4 - 5 i}{41}

= \frac{4 - 5 i}{41}

Rewrite in standard complex form:

\frac{4}{41} - \frac{5}{41} i

= \frac{4}{41} - \frac{5}{41} i

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Frequently Asked Questions (FAQ)

What is 1/(4+5i) ?
The solution to 1/(4+5i) is 4/41-5/41 i