What is (2+2i)/(-sqrt(3)+i) ?

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

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simplify (2+2i)/(-sqrt(3)+i)

simplify

\frac{2 + 2 i}{- 3 + i}

\frac{- 3 + 1}{2} - \frac{1 + 3}{2} i

Solution steps

\frac{2 + 2 i}{- 3 + i}

Multiply by the conjugate

\frac{- 3 - i}{- 3 - i}

= \frac{( 2 + 2 i ) ( - 3 - i )}{( - 3 + i ) ( - 3 - i )}

Simplify

\frac{( 2 + 2 i ) ( - 3 - i )}{( - 3 + i ) ( - 3 - i )} : \frac{- 2 3 + 2 - 2 i ( 1 + 3 )}{4}

= \frac{- 2 3 + 2 - 2 i ( 1 + 3 )}{4}

Rewrite in standard complex form:

\frac{- 3 + 1}{2} - \frac{1 + 3}{2} i

= \frac{- 3 + 1}{2} - \frac{1 + 3}{2} i

\frac{5 - 6 i}{5 + i}

- 16 \times 3

- 16 \times 2

(- 6 + 7 i) + (14 - 6 i)

4 x^{3} - 24 x^{2} - 60 x

What is (2+2i)/(-sqrt(3)+i) ?
The solution to (2+2i)/(-sqrt(3)+i) is (-sqrt(3)+1)/2-(1+sqrt(3))/2 i