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

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

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

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 3 + 2 i ) ( 5 + i )}{( 5 - i ) ( 5 + i )} : \frac{13 + 13 i}{26}

= \frac{13 + 13 i}{26}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{13}{26} + \frac{13}{26} i

Simplify

\frac{13}{26} + \frac{13}{26} i : \frac{1}{2} + \frac{1}{2} i

= \frac{1}{2} + \frac{1}{2} i

\frac{6}{63}

\frac{3}{4} 48

16 \div \frac{2}{3}

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

(1 + 4 i)^{3}