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

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

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

simplify

(- 1 + 3 i)^{2}

- 2 - 23 i

Solution steps

(- 1 + 3 i)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

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

= - 23 i - 2

Rewrite in standard complex form:

- 2 - 23 i

= - 2 - 23 i

(- 1 + 3 i)^{3}

\frac{5}{18}

\frac{5}{15}

\frac{13 + 9 i}{- 2 - i}

- x^{3} + 4 x^{2} - 5 x + 2