Algebra Examples

$2 i^{4} - 2 i^{3} + 1^{2} - i + 2$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{4}$ as $1$ .

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Step 1.1.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

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

Step 1.1.2

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

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

Step 1.1.3

Raise $- 1$ to the power of $2$ .

$2 \cdot 1 - 2 i^{3} + 1^{2} - i + 2$

$2 \cdot 1 - 2 i^{3} + 1^{2} - i + 2$

Step 1.2

Multiply $2$ by $1$ .

$2 - 2 i^{3} + 1^{2} - i + 2$

Step 1.3

Factor out $i^{2}$ .

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

Step 1.4

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

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

Step 1.5

Rewrite $- 1 i$ as $- i$ .

$2 - 2 (- i) + 1^{2} - i + 2$

Step 1.6

Multiply $- 1$ by $- 2$ .

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

Step 1.7

One to any power is one.

$2 + 2 i + 1 - i + 2$

$2 + 2 i + 1 - i + 2$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2$ and $1$ .

$3 + 2 i - i + 2$

Step 2.2

Add $3$ and $2$ .

$5 + 2 i - i$

Step 2.3

Subtract $i$ from $2 i$ .

$5 + i$

$5 + i$

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