What is (5-2i)/(4+2i) ?

The solution to (5-2i)/(4+2i) is 4/5-9/10 i

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simplify (5-2i)/(4+2i)

simplify

\frac{5 - 2 i}{4 + 2 i}

\frac{4}{5} - \frac{9}{10} i

Solution steps

\frac{5 - 2 i}{4 + 2 i}

Multiply by the conjugate

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

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

Simplify

\frac{( 5 - 2 i ) ( 4 - 2 i )}{( 4 + 2 i ) ( 4 - 2 i )} : \frac{16 - 18 i}{20}

= \frac{16 - 18 i}{20}

Apply the fraction rule:

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

= \frac{16}{20} + \frac{- 18}{20} i

Simplify

\frac{16}{20} + \frac{- 18}{20} i : \frac{4}{5} - \frac{9}{10} i

= \frac{4}{5} - \frac{9}{10} i

\frac{( 3 y + 4 )}{5} - \frac{( y + 2 )}{2} = \frac{( 4 y - 1 )}{10}

5^{\frac{1}{2}} \cdot 4 5^{\frac{1}{2}}

x^{4} - x^{3} - x + 1

4 x^{2} - 4 x = 0

x^{2} - 2 x - 143