Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Factor out $i^{2}$ .

$4 + i^{2} \cdot i + 5 + i^{5}$

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Factor out $i^{4}$ .

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

Step 2.5

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

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Step 2.5.1

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

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

Step 2.5.2

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

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

Step 2.5.3

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

$4 - i + 5 + 1 i$

$4 - i + 5 + 1 i$

Step 2.6

Multiply $i$ by $1$ .

$4 - i + 5 + i$

$4 - i + 5 + i$

Step 3

Simplify by adding terms.

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Step 3.1

Add $4$ and $5$ .

$9 - i + i$

Step 3.2

Add $- i$ and $i$ .

$9 + 0$

Step 3.3

Add $9$ and $0$ .

$9$

$9$

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