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

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