Simplify (-i square root of 2)(i square root of 2)

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

Multiply $(- i \sqrt{2}) (i \sqrt{2})$ .

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

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

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

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

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

$- i^{1 + 1} \sqrt{2} \sqrt{2}$

Add $1$ and $1$ .

$- i^{2} \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

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

$- i^{2} {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$- i^{2} {\sqrt{2}}^{2}$

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

$- - 1 {\sqrt{2}}^{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 {\sqrt{2}}^{2}$

Multiply ${\sqrt{2}}^{2}$ by $1$ .

${\sqrt{2}}^{2}$

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

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

${(2^{\frac{1}{2}})}^{2}$

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

$2^{\frac{1}{2} \cdot 2}$

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

$2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2^{\frac{2}{2}}$

Rewrite the expression.

$2^{1}$

Evaluate the exponent.

$2$