Finite Math Examples

${(- \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

${(- (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2

Combine and simplify the denominator.

Tap for more steps...

Step 1.2.1

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

${(- \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.2

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

${(- \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.3

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

${(- \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.4

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

${(- \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.5

Add $1$ and $1$ .

${(- \frac{\sqrt{2}}{{\sqrt{2}}^{2}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.6

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

Tap for more steps...

Step 1.2.6.1

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

${(- \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.6.2

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

${(- \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.6.3

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

${(- \frac{\sqrt{2}}{2^{\frac{2}{2}}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.6.4.1

Cancel the common factor.

${(- \frac{\sqrt{2}}{2^{\frac{2}{2}}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.6.4.2

Rewrite the expression.

${(- \frac{\sqrt{2}}{2^{1}} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.2.6.5

Evaluate the exponent.

${(- \frac{\sqrt{2}}{2} + \frac{1}{\sqrt{2}} \cdot i)}^{123}$

Step 1.3

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

${(- \frac{\sqrt{2}}{2} + \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \cdot i)}^{123}$

Step 1.4

Combine and simplify the denominator.

Tap for more steps...

Step 1.4.1

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} \cdot i)}^{123}$

Step 1.4.2

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} \cdot i)}^{123}$

Step 1.4.3

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} \cdot i)}^{123}$

Step 1.4.4

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} \cdot i)}^{123}$

Step 1.4.5

Add $1$ and $1$ .

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{{\sqrt{2}}^{2}} \cdot i)}^{123}$

Step 1.4.6

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

Tap for more steps...

Step 1.4.6.1

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} \cdot i)}^{123}$

Step 1.4.6.2

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} \cdot i)}^{123}$

Step 1.4.6.3

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

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2^{\frac{2}{2}}} \cdot i)}^{123}$

Step 1.4.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.4.6.4.1

Cancel the common factor.

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2^{\frac{2}{2}}} \cdot i)}^{123}$

Step 1.4.6.4.2

Rewrite the expression.

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2^{1}} \cdot i)}^{123}$

Step 1.4.6.5

Evaluate the exponent.

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} \cdot i)}^{123}$

Step 1.5

Combine $\frac{\sqrt{2}}{2}$ and $i$ .

${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2})}^{123}$

Step 2

The degree cannot be determined because ${(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2})}^{123}$ is not a polynomial.

Not a polynomial