Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Factor out $i^{2}$ .

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

Step 1.2

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

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

Step 1.3

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

$(2 - 3 (- i)) (1 + i)$

Step 1.4

Multiply $- 1$ by $- 3$ .

$(2 + 3 i) (1 + i)$

$(2 + 3 i) (1 + i)$

Step 2

Expand $(2 + 3 i) (1 + i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 (1 + i) + 3 i (1 + i)$

Step 2.2

Apply the distributive property.

$2 \cdot 1 + 2 i + 3 i (1 + i)$

Step 2.3

Apply the distributive property.

$2 \cdot 1 + 2 i + 3 i \cdot 1 + 3 i i$

$2 \cdot 1 + 2 i + 3 i \cdot 1 + 3 i i$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $1$ .

$2 + 2 i + 3 i \cdot 1 + 3 i i$

Step 3.1.2

Multiply $3$ by $1$ .

$2 + 2 i + 3 i + 3 i i$

Step 3.1.3

Multiply $3 i i$ .

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Step 3.1.3.1

Raise $i$ to the power of $1$ .

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

Step 3.1.3.2

Raise $i$ to the power of $1$ .

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

Step 3.1.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.1.3.4

Add $1$ and $1$ .

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

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

Step 3.1.4

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

$2 + 2 i + 3 i + 3 \cdot - 1$

Step 3.1.5

Multiply $3$ by $- 1$ .

$2 + 2 i + 3 i - 3$

$2 + 2 i + 3 i - 3$

Step 3.2

Subtract $3$ from $2$ .

$- 1 + 2 i + 3 i$

Step 3.3

Add $2 i$ and $3 i$ .

$- 1 + 5 i$

$- 1 + 5 i$

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