What is 6/((2+i)(3+5i)(1-i)) ?

The solution to 6/((2+i)(3+5i)(1-i)) is 21/85-18/85 i

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simplify 6/((2+i)(3+5i)(1-i))

simplify

\frac{6}{( 2 + i ) ( 3 + 5 i ) ( 1 - i )}

\frac{21}{85} - \frac{18}{85} i

Solution steps

\frac{6}{( 2 + i ) ( 3 + 5 i ) ( 1 - i )}

(2 + i) (3 + 5 i) (1 - i) = 14 + 12 i

= \frac{6}{14 + 12 i}

Multiply by the conjugate

\frac{14 - 12 i}{14 - 12 i}

= \frac{6 ( 14 - 12 i )}{( 14 + 12 i ) ( 14 - 12 i )}

Simplify

\frac{6 ( 14 - 12 i )}{( 14 + 12 i ) ( 14 - 12 i )} : \frac{84 - 72 i}{340}

= \frac{84 - 72 i}{340}

Apply the fraction rule:

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

= \frac{84}{340} + \frac{- 72}{340} i

Simplify

\frac{84}{340} + \frac{- 72}{340} i : \frac{21}{85} - \frac{18}{85} i

= \frac{21}{85} - \frac{18}{85} i

(4 a^{2} + 2 ab + 5 b) + (6 a^{2} - 7 ab)

\frac{1}{3 + 5}

(- 5.3) (1.1)

8 (1 + 6 p)

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

What is 6/((2+i)(3+5i)(1-i)) ?
The solution to 6/((2+i)(3+5i)(1-i)) is 21/85-18/85 i