Trigonometry Examples

$3 (4 i - 7) + 5 i (3 i - 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 (4 i) + 3 \cdot - 7 + 5 i (3 i - 2)$

Step 1.2

Multiply $4$ by $3$ .

$12 i + 3 \cdot - 7 + 5 i (3 i - 2)$

Step 1.3

Multiply $3$ by $- 7$ .

$12 i - 21 + 5 i (3 i - 2)$

Step 1.4

Apply the distributive property.

$12 i - 21 + 5 i (3 i) + 5 i \cdot - 2$

Step 1.5

Multiply $5 i (3 i)$ .

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Step 1.5.1

Multiply $3$ by $5$ .

$12 i - 21 + 15 i i + 5 i \cdot - 2$

Step 1.5.2

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

$12 i - 21 + 15 (i^{1} i) + 5 i \cdot - 2$

Step 1.5.3

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

$12 i - 21 + 15 (i^{1} i^{1}) + 5 i \cdot - 2$

Step 1.5.4

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

$12 i - 21 + 15 i^{1 + 1} + 5 i \cdot - 2$

Step 1.5.5

Add $1$ and $1$ .

$12 i - 21 + 15 i^{2} + 5 i \cdot - 2$

$12 i - 21 + 15 i^{2} + 5 i \cdot - 2$

Step 1.6

Multiply $- 2$ by $5$ .

$12 i - 21 + 15 i^{2} - 10 i$

Step 1.7

Simplify each term.

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Step 1.7.1

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

$12 i - 21 + 15 \cdot - 1 - 10 i$

Step 1.7.2

Multiply $15$ by $- 1$ .

$12 i - 21 - 15 - 10 i$

$12 i - 21 - 15 - 10 i$

$12 i - 21 - 15 - 10 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $10 i$ from $12 i$ .

$- 21 - 15 + 2 i$

Step 2.2

Subtract $15$ from $- 21$ .

$- 36 + 2 i$

$- 36 + 2 i$

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