Trigonometry Examples

$3 i (2 i^{2} - 5 i)$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Multiply $2$ by $- 1$ .

$3 i (- 2 - 5 i)$

$3 i (- 2 - 5 i)$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- 2$ by $3$ .

$- 6 i + 3 i (- 5 i)$

$- 6 i + 3 i (- 5 i)$

Step 3

Multiply $3 i (- 5 i)$ .

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Step 3.1

Multiply $- 5$ by $3$ .

$- 6 i - 15 i i$

Step 3.2

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

$- 6 i - 15 (i^{1} i)$

Step 3.3

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

$- 6 i - 15 (i^{1} i^{1})$

Step 3.4

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

$- 6 i - 15 i^{1 + 1}$

Step 3.5

Add $1$ and $1$ .

$- 6 i - 15 i^{2}$

$- 6 i - 15 i^{2}$

Step 4

Simplify each term.

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Step 4.1

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

$- 6 i - 15 \cdot - 1$

Step 4.2

Multiply $- 15$ by $- 1$ .

$- 6 i + 15$

$- 6 i + 15$

Step 5

Reorder $- 6 i$ and $15$ .

$15 - 6 i$

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