Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $2 i$ .

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

Step 1.2

Raise $2$ to the power of $2$ .

$4 i^{2} - {(\sqrt{3} i)}^{2}$

Step 1.3

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

$4 \cdot - 1 - {(\sqrt{3} i)}^{2}$

Step 1.4

Multiply $4$ by $- 1$ .

$- 4 - {(\sqrt{3} i)}^{2}$

Step 1.5

Apply the product rule to $\sqrt{3} i$ .

$- 4 - ({\sqrt{3}}^{2} i^{2})$

Step 1.6

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

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Step 1.6.1

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

$- 4 - ({(3^{\frac{1}{2}})}^{2} i^{2})$

Step 1.6.2

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

$- 4 - (3^{\frac{1}{2} \cdot 2} i^{2})$

Step 1.6.3

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

$- 4 - (3^{\frac{2}{2}} i^{2})$

Step 1.6.4

Cancel the common factor of $2$ .

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Step 1.6.4.1

Cancel the common factor.

$- 4 - (3^{\frac{2}{2}} i^{2})$

Step 1.6.4.2

Rewrite the expression.

$- 4 - (3^{1} i^{2})$

Step 1.6.5

Evaluate the exponent.

$- 4 - (3 i^{2})$

Step 1.7

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

$- 4 - (3 \cdot - 1)$

Step 1.8

Multiply $- (3 \cdot - 1)$ .

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Step 1.8.1

Multiply $3$ by $- 1$ .

$- 4 - - 3$

Step 1.8.2

Multiply $- 1$ by $- 3$ .

$- 4 + 3$

Step 2

Add $- 4$ and $3$ .

$- 1$