What is (7-i)/(2+10i) ?

The solution to (7-i)/(2+10i) is 1/26-9/13 i

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simplify (7-i)/(2+10i)

simplify

\frac{7 - i}{2 + 10 i}

\frac{1}{26} - \frac{9}{13} i

Solution steps

\frac{7 - i}{2 + 10 i}

Multiply by the conjugate

\frac{2 - 10 i}{2 - 10 i}

= \frac{( 7 - i ) ( 2 - 10 i )}{( 2 + 10 i ) ( 2 - 10 i )}

Simplify

\frac{( 7 - i ) ( 2 - 10 i )}{( 2 + 10 i ) ( 2 - 10 i )} : \frac{4 - 72 i}{104}

= \frac{4 - 72 i}{104}

Apply the fraction rule:

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

= \frac{4}{104} + \frac{- 72}{104} i

Simplify

\frac{4}{104} + \frac{- 72}{104} i : \frac{1}{26} - \frac{9}{13} i

= \frac{1}{26} - \frac{9}{13} i

(a - 1) (a - 2)

(n - 8) 2

\frac{3}{3 - 1}

(2 n^{3})^{4}

\frac{3}{4 a b ^{3}} + \frac{c}{a ^{2} b}