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

The solution to ((2+i))/((2-2i)) is 1/4+3/4 i

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

simplify

\frac{( 2 + i )}{( 2 - 2 i )}

\frac{1}{4} + \frac{3}{4} i

Solution steps

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

Multiply by the conjugate

\frac{2 + 2 i}{2 + 2 i}

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

Simplify

\frac{( 2 + i ) ( 2 + 2 i )}{( 2 - 2 i ) ( 2 + 2 i )} : \frac{2 + 6 i}{8}

= \frac{2 + 6 i}{8}

Apply the fraction rule:

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

= \frac{2}{8} + \frac{6}{8} i

Simplify

\frac{2}{8} + \frac{6}{8} i : \frac{1}{4} + \frac{3}{4} i

= \frac{1}{4} + \frac{3}{4} i

ln (e^{- x^{2}})

\frac{20 z ^{- 9}}{( - 5 z ) ^{2}}

\frac{3 x}{5 y} + \frac{4}{5 y}

(3 + 2 i) (2 - 3 i)

\frac{1}{x ^{2}} - \frac{1}{x ^{2} + x}