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

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

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simplify (1-isqrt(3))^2

simplify

(1 - i 3)^{2}

- 2 - 23 i

Solution steps

(1 - i 3)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= - 23 i - 2

Rewrite in standard complex form:

- 2 - 23 i

= - 2 - 23 i

\frac{x ^{2} + 3 x + 2}{x ^{2} - 4}

(- y + 3)^{2}

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

\frac{1}{x - 2} - 1

\frac{9}{120}