What is (3+2i)/(1+5i) ?

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

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simplify (3+2i)/(1+5i)

simplify

\frac{3 + 2 i}{1 + 5 i}

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

Solution steps

\frac{3 + 2 i}{1 + 5 i}

Multiply by the conjugate

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

= \frac{( 3 + 2 i ) ( 1 - 5 i )}{( 1 + 5 i ) ( 1 - 5 i )}

Simplify

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

(- x - 4)^{2} - (- x - 4) - 1

25 (x - y)^{2} - 4 (x + y)^{2}

4 r^{2} + 20 r + 25

2 + \frac{3}{8}