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Popular >

simplify 1/(1+3i)

Solution

simplify

\frac{1}{1 + 3 i}

Solution

\frac{1}{10} - \frac{3}{10} i

Solution steps

\frac{1}{1 + 3 i}

Multiply by the conjugate

\frac{1 - 3 i}{1 - 3 i}

= \frac{1 \cdot ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )}

Simplify

\frac{1 \cdot ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )} : \frac{1 - 3 i}{10}

= \frac{1 - 3 i}{10}

Rewrite in standard complex form:

\frac{1}{10} - \frac{3}{10} i

= \frac{1}{10} - \frac{3}{10} i

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Frequently Asked Questions (FAQ)

What is 1/(1+3i) ?
The solution to 1/(1+3i) is 1/10-3/10 i