Algebra Examples

$5 i^{4} + 3 i^{3} - 4 i^{2} + 5 i - 3$

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 ${(i^{2})}^{2}$ .

$5 {(i^{2})}^{2} + 3 i^{3} - 4 i^{2} + 5 i - 3$

Step 1.1.2

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

$5 {(- 1)}^{2} + 3 i^{3} - 4 i^{2} + 5 i - 3$

Step 1.1.3

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

$5 \cdot 1 + 3 i^{3} - 4 i^{2} + 5 i - 3$

$5 \cdot 1 + 3 i^{3} - 4 i^{2} + 5 i - 3$

Step 1.2

Multiply $5$ by $1$ .

$5 + 3 i^{3} - 4 i^{2} + 5 i - 3$

Step 1.3

Factor out $i^{2}$ .

$5 + 3 (i^{2} \cdot i) - 4 i^{2} + 5 i - 3$

Step 1.4

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

$5 + 3 (- 1 \cdot i) - 4 i^{2} + 5 i - 3$

Step 1.5

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

$5 + 3 (- i) - 4 i^{2} + 5 i - 3$

Step 1.6

Multiply $- 1$ by $3$ .

$5 - 3 i - 4 i^{2} + 5 i - 3$

Step 1.7

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

$5 - 3 i - 4 \cdot - 1 + 5 i - 3$

Step 1.8

Multiply $- 4$ by $- 1$ .

$5 - 3 i + 4 + 5 i - 3$

$5 - 3 i + 4 + 5 i - 3$

Step 2

Simplify by adding terms.

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Step 2.1

Add $5$ and $4$ .

$9 - 3 i + 5 i - 3$

Step 2.2

Subtract $3$ from $9$ .

$6 - 3 i + 5 i$

Step 2.3

Add $- 3 i$ and $5 i$ .

$6 + 2 i$

$6 + 2 i$

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