What is ((1+i))/((2-5i)) ?

The solution to ((1+i))/((2-5i)) is -3/29+7/29 i

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simplify ((1+i))/((2-5i))

simplify

\frac{( 1 + i )}{( 2 - 5 i )}

- \frac{3}{29} + \frac{7}{29} i

Solution steps

\frac{1 + i}{2 - 5 i}

Multiply by the conjugate

\frac{2 + 5 i}{2 + 5 i}

= \frac{( 1 + i ) ( 2 + 5 i )}{( 2 - 5 i ) ( 2 + 5 i )}

Simplify

\frac{( 1 + i ) ( 2 + 5 i )}{( 2 - 5 i ) ( 2 + 5 i )} : \frac{- 3 + 7 i}{29}

= \frac{- 3 + 7 i}{29}

Rewrite in standard complex form:

- \frac{3}{29} + \frac{7}{29} i

= - \frac{3}{29} + \frac{7}{29} i

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