Algebra Examples

$(5 - i^{7}) - (9 + i^{10})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

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Step 1.1.1

Factor out $i^{4}$ .

$5 - (i^{4} i^{3}) - (9 + i^{10})$

Step 1.1.2

Factor out $i^{2}$ .

$5 - (i^{4} (i^{2} \cdot i)) - (9 + i^{10})$

$5 - (i^{4} (i^{2} \cdot i)) - (9 + i^{10})$

Step 1.2

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

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Step 1.2.1

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

$5 - ({(i^{2})}^{2} (i^{2} \cdot i)) - (9 + i^{10})$

Step 1.2.2

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

$5 - ({(- 1)}^{2} (i^{2} \cdot i)) - (9 + i^{10})$

Step 1.2.3

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

$5 - (1 (i^{2} \cdot i)) - (9 + i^{10})$

$5 - (1 (i^{2} \cdot i)) - (9 + i^{10})$

Step 1.3

Multiply $i^{2} \cdot i$ by $1$ .

$5 - (i^{2} \cdot i) - (9 + i^{10})$

Step 1.4

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

$5 - (- 1 \cdot i) - (9 + i^{10})$

Step 1.5

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

$5 - - i - (9 + i^{10})$

Step 1.6

Multiply $- 1$ by $- 1$ .

$5 + 1 i - (9 + i^{10})$

Step 1.7

Multiply $i$ by $1$ .

$5 + i - (9 + i^{10})$

Step 1.8

Simplify each term.

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Step 1.8.1

Rewrite $i^{10}$ as ${(i^{4})}^{2} i^{2}$ .

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Step 1.8.1.1

Factor out $i^{8}$ .

$5 + i - (9 + i^{8} i^{2})$

Step 1.8.1.2

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$5 + i - (9 + {(i^{4})}^{2} i^{2})$

$5 + i - (9 + {(i^{4})}^{2} i^{2})$

Step 1.8.2

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

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Step 1.8.2.1

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

$5 + i - (9 + {({(i^{2})}^{2})}^{2} i^{2})$

Step 1.8.2.2

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

$5 + i - (9 + {({(- 1)}^{2})}^{2} i^{2})$

Step 1.8.2.3

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

$5 + i - (9 + 1^{2} i^{2})$

$5 + i - (9 + 1^{2} i^{2})$

Step 1.8.3

One to any power is one.

$5 + i - (9 + 1 i^{2})$

Step 1.8.4

Multiply $i^{2}$ by $1$ .

$5 + i - (9 + i^{2})$

Step 1.8.5

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

$5 + i - (9 - 1)$

$5 + i - (9 - 1)$

Step 1.9

Subtract $1$ from $9$ .

$5 + i - 1 \cdot 8$

Step 1.10

Multiply $- 1$ by $8$ .

$5 + i - 8$

$5 + i - 8$

Step 2

Subtract $8$ from $5$ .

$- 3 + i$

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