Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Multiply $- 5$ by $- 1$ .

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

Step 1.3

Factor out $i^{2}$ .

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

Step 1.4

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

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

Step 1.5

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

$1 + 3 i + 5 + 4 - 2 i - - i$

Step 1.6

Multiply $- 1$ by $- 1$ .

$1 + 3 i + 5 + 4 - 2 i + 1 i$

Step 1.7

Multiply $i$ by $1$ .

$1 + 3 i + 5 + 4 - 2 i + i$

$1 + 3 i + 5 + 4 - 2 i + i$

Step 2

Simplify by adding terms.

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Step 2.1

Add $1$ and $5$ .

$6 + 3 i + 4 - 2 i + i$

Step 2.2

Add $6$ and $4$ .

$10 + 3 i - 2 i + i$

Step 2.3

Subtract $2 i$ from $3 i$ .

$10 + i + i$

Step 2.4

Add $i$ and $i$ .

$10 + 2 i$

$10 + 2 i$

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