Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $- 1$ by $1$ .

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

Step 1.3

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

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.3.2

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

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

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $1$ from $1$ .

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

Step 2.2

Simplify the expression.

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Step 2.2.1

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

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

Step 2.2.2

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

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

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

Step 2.3

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

$2 i \sqrt{2}$

$2 i \sqrt{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$