Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Subtract $\sqrt{2}$ from $\sqrt{2}$ .

$\frac{- i \sqrt{2} + 0 - \sqrt{2} i}{2}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Add $- i \sqrt{2}$ and $0$ .

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

Step 2.3.2

Reorder the factors of $- \sqrt{2} i$ .

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

Step 2.4

Subtract $i \sqrt{2}$ from $- i \sqrt{2}$ .

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

Step 2.5

Cancel the common factor of $- 2$ and $2$ .

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Step 2.5.1

Factor $2$ out of $- 2 i \sqrt{2}$ .

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

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $2$ .

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

Step 2.5.2.2

Cancel the common factor.

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

Step 2.5.2.3

Rewrite the expression.

$\frac{- i \sqrt{2}}{1}$

Step 2.5.2.4

Divide $- i \sqrt{2}$ by $1$ .

$- i \sqrt{2}$