What is (3+i)/(5-2i) ?

The solution to (3+i)/(5-2i) is 13/29+11/29 i

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simplify (3+i)/(5-2i)

simplify

\frac{3 + i}{5 - 2 i}

\frac{13}{29} + \frac{11}{29} i

Solution steps

\frac{3 + i}{5 - 2 i}

Multiply by the conjugate

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

= \frac{( 3 + i ) ( 5 + 2 i )}{( 5 - 2 i ) ( 5 + 2 i )}

Simplify

\frac{( 3 + i ) ( 5 + 2 i )}{( 5 - 2 i ) ( 5 + 2 i )} : \frac{13 + 11 i}{29}

= \frac{13 + 11 i}{29}

Rewrite in standard complex form:

\frac{13}{29} + \frac{11}{29} i

= \frac{13}{29} + \frac{11}{29} i

\frac{- i}{1 + i}

2.0 1^{2}

(2 + i) (- 3 - i)

3 x^{5} y^{2}

a^{- 4} b^{- \frac{1}{2}}