What is ((1+i)^3)/((sqrt(3)+i)^2) ?

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

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simplify ((1+i)^3)/((sqrt(3)+i)^2)

simplify

\frac{( 1 + i ) ^{3}}{( 3 + i ) ^{2}}

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

Solution steps

\frac{( 1 + i ) ^{3}}{( 3 + i ) ^{2}}

Expand

(1 + i)^{3} : 2 i - 2

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

Expand

(3 + i)^{2} : 23 i + 2

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

Factor

2 i - 2 : 2 (i - 1)

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

Factor out common term

2 : 2 (3 i + 1)

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

Cancel the common factor:

2

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

Simplify

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

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

\frac{( 5 d ^{- 3} ) ^{2}}{- 20 d ^{- 10}}

(2 x - 5 x^{2}) (7 x^{3} - 3 x)

(3 - 2 i) (4 + 5 i)

(x^{3})^{\frac{1}{3}}

y - (- 3)

What is ((1+i)^3)/((sqrt(3)+i)^2) ?
The solution to ((1+i)^3)/((sqrt(3)+i)^2) is (-1+sqrt(3))/4+(sqrt(3)+1)/4 i