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

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

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

simplify

(- 2 + - 3)^{2}

1 - 43 i

Solution steps

(- 2 + - 3)^{2}

Apply Perfect Square Formula:

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

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

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

(- 2)^{2} + 2 (- 2) - 3 + (- 3)^{2} = - 43 i + 1

= - 43 i + 1

Rewrite in standard complex form:

1 - 43 i

= 1 - 43 i

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