What is ((-1+isqrt(3))/2)^2 ?

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

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simplify ((-1+isqrt(3))/2)^2

simplify

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

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

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

2^{2} = 4

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

Expand

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

= \frac{- 2 3 i - 2}{4}

Factor out common term

- 2 : - 2 (3 i + 1)

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

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

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

Simplify

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

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

1.6 \cdot 1 0^{5}

1.6 \cdot 1 0^{6}

5 l mn - 6 m l + 7 l m + 8 mn l - 4 ln (x)

2 s^{3} + 18 s

⌈ 2.5 ⌉

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