Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $3$ by $2$ .

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

Step 1.3

Multiply $3$ by $3$ .

$6 + 9 i - i (2 - 3 i)$

Step 1.4

Apply the distributive property.

$6 + 9 i - i \cdot 2 - i (- 3 i)$

Step 1.5

Multiply $2$ by $- 1$ .

$6 + 9 i - 2 i - i (- 3 i)$

Step 1.6

Multiply $- i (- 3 i)$ .

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Step 1.6.1

Multiply $- 3$ by $- 1$ .

$6 + 9 i - 2 i + 3 i i$

Step 1.6.2

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

$6 + 9 i - 2 i + 3 (i^{1} i)$

Step 1.6.3

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

$6 + 9 i - 2 i + 3 (i^{1} i^{1})$

Step 1.6.4

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

$6 + 9 i - 2 i + 3 i^{1 + 1}$

Step 1.6.5

Add $1$ and $1$ .

$6 + 9 i - 2 i + 3 i^{2}$

$6 + 9 i - 2 i + 3 i^{2}$

Step 1.7

Simplify each term.

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Step 1.7.1

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

$6 + 9 i - 2 i + 3 \cdot - 1$

Step 1.7.2

Multiply $3$ by $- 1$ .

$6 + 9 i - 2 i - 3$

$6 + 9 i - 2 i - 3$

$6 + 9 i - 2 i - 3$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3$ from $6$ .

$3 + 9 i - 2 i$

Step 2.2

Subtract $2 i$ from $9 i$ .

$3 + 7 i$

$3 + 7 i$

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