Simplify (i- square root of 3)^2

${(i - \sqrt{3})}^{2}$

Rewrite ${(i - \sqrt{3})}^{2}$ as $(i - \sqrt{3}) (i - \sqrt{3})$ .

$(i - \sqrt{3}) (i - \sqrt{3})$

Expand $(i - \sqrt{3}) (i - \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$i (i - \sqrt{3}) - \sqrt{3} (i - \sqrt{3})$

Apply the distributive property.

$i i + i (- \sqrt{3}) - \sqrt{3} (i - \sqrt{3})$

Apply the distributive property.

$i i + i (- \sqrt{3}) - \sqrt{3} i - \sqrt{3} (- \sqrt{3})$

Simplify and combine like terms.

Simplify each term.

Multiply $i i$ .

Raise $i$ to the power of $1$ .

$i^{1} i + i (- \sqrt{3}) - \sqrt{3} i - \sqrt{3} (- \sqrt{3})$

Raise $i$ to the power of $1$ .

$i^{1} i^{1} + i (- \sqrt{3}) - \sqrt{3} i - \sqrt{3} (- \sqrt{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$i^{1 + 1} + i (- \sqrt{3}) - \sqrt{3} i - \sqrt{3} (- \sqrt{3})$

Add $1$ and $1$ .

$i^{2} + i (- \sqrt{3}) - \sqrt{3} i - \sqrt{3} (- \sqrt{3})$

Rewrite $i^{2}$ as $- 1$ .

$- 1 + i (- \sqrt{3}) - \sqrt{3} i - \sqrt{3} (- \sqrt{3})$

Multiply $- \sqrt{3} (- \sqrt{3})$ .

Multiply $- 1$ by $- 1$ .

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + 1 \sqrt{3} \sqrt{3}$

Multiply $\sqrt{3}$ by $1$ .

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + \sqrt{3} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + {\sqrt{3}}^{1} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + {\sqrt{3}}^{1} {\sqrt{3}}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + 3^{1}$

Evaluate the exponent.

$- 1 + i (- \sqrt{3}) - \sqrt{3} i + 3$

Add $- 1$ and $3$ .

$i (- \sqrt{3}) - \sqrt{3} i + 2$

Reorder the factors of $- \sqrt{3} i$ .

$i (- \sqrt{3}) - i \sqrt{3} + 2$

Subtract $i \sqrt{3}$ from $i (- \sqrt{3})$ .

Reorder $i$ and $- 1$ .

$- 1 \cdot i \sqrt{3} - i \sqrt{3} + 2$

Subtract $i \sqrt{3}$ from $- 1 \cdot i \sqrt{3}$ .

$- 2 i \sqrt{3} + 2$

Reorder $- 2 i \sqrt{3}$ and $2$ .

$2 - 2 i \sqrt{3}$

Simplify (i- square root of 3)^2

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