simplify 5/(2+4i)

Solution

simplify

\frac{5}{2 + 4 i}

\frac{1}{2} - i

Solution steps

\frac{5}{2 + 4 i}

Multiply by the conjugate

\frac{2 - 4 i}{2 - 4 i}

= \frac{5 ( 2 - 4 i )}{( 2 + 4 i ) ( 2 - 4 i )}

Simplify

\frac{5 ( 2 - 4 i )}{( 2 + 4 i ) ( 2 - 4 i )} : \frac{10 - 20 i}{20}

= \frac{10 - 20 i}{20}

Apply the fraction rule:

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

= \frac{10}{20} + \frac{- 20}{20} i

Simplify

\frac{10}{20} + \frac{- 20}{20} i : \frac{1}{2} - i

= \frac{1}{2} - i

(2 x^{4} + 3 x^{3}) (2 x^{4} - 3 x^{3})

(2 + 3 x)^{2}

(4 a^{3} c - 7 a^{2} b - 2 c) (- 3 a c^{4})

(3 x - 4) (x^{2} - 5 x - 1)

100 x^{2} - z^{2}