Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 i \cdot 4 + 3 i (- i) + i (6 + 2 i)$

Step 1.2

Multiply $4$ by $3$ .

$12 i + 3 i (- i) + i (6 + 2 i)$

Step 1.3

Multiply $3 i (- i)$ .

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Step 1.3.1

Multiply $- 1$ by $3$ .

$12 i - 3 i i + i (6 + 2 i)$

Step 1.3.2

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

$12 i - 3 (i^{1} i) + i (6 + 2 i)$

Step 1.3.3

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

$12 i - 3 (i^{1} i^{1}) + i (6 + 2 i)$

Step 1.3.4

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

$12 i - 3 i^{1 + 1} + i (6 + 2 i)$

Step 1.3.5

Add $1$ and $1$ .

$12 i - 3 i^{2} + i (6 + 2 i)$

$12 i - 3 i^{2} + i (6 + 2 i)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$12 i - 3 \cdot - 1 + i (6 + 2 i)$

Step 1.4.2

Multiply $- 3$ by $- 1$ .

$12 i + 3 + i (6 + 2 i)$

$12 i + 3 + i (6 + 2 i)$

Step 1.5

Apply the distributive property.

$12 i + 3 + i \cdot 6 + i (2 i)$

Step 1.6

Move $6$ to the left of $i$ .

$12 i + 3 + 6 \cdot i + i (2 i)$

Step 1.7

Multiply $i (2 i)$ .

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Step 1.7.1

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

$12 i + 3 + 6 \cdot i + 2 (i^{1} i)$

Step 1.7.2

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

$12 i + 3 + 6 \cdot i + 2 (i^{1} i^{1})$

Step 1.7.3

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

$12 i + 3 + 6 \cdot i + 2 i^{1 + 1}$

Step 1.7.4

Add $1$ and $1$ .

$12 i + 3 + 6 \cdot i + 2 i^{2}$

$12 i + 3 + 6 \cdot i + 2 i^{2}$

Step 1.8

Simplify each term.

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Step 1.8.1

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

$12 i + 3 + 6 i + 2 \cdot - 1$

Step 1.8.2

Multiply $2$ by $- 1$ .

$12 i + 3 + 6 i - 2$

$12 i + 3 + 6 i - 2$

$12 i + 3 + 6 i - 2$

Step 2

Simplify by adding terms.

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Step 2.1

Add $12 i$ and $6 i$ .

$3 + 18 i - 2$

Step 2.2

Subtract $2$ from $3$ .

$1 + 18 i$

$1 + 18 i$

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