What is 1/(1+3i)+1/(1+8i) ?

The solution to 1/(1+3i)+1/(1+8i) is 3/26-11/26 i

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simplify 1/(1+3i)+1/(1+8i)

simplify

\frac{1}{1 + 3 i} + \frac{1}{1 + 8 i}

\frac{3}{26} - \frac{11}{26} i

Solution steps

\frac{1}{1 + 3 i} + \frac{1}{1 + 8 i}

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

\frac{1}{1 + 8 i} = \frac{1 - 8 i}{65}

= \frac{1 - 3 i}{10} + \frac{1 - 8 i}{65}

Join

\frac{1 - 3 i}{10} + \frac{1 - 8 i}{65} : \frac{- 11 i + 3}{26}

= \frac{- 11 i + 3}{26}

Rewrite in standard complex form:

\frac{3}{26} - \frac{11}{26} i

= \frac{3}{26} - \frac{11}{26} i

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