Trigonometry Examples

$(2 i + 5) (i - 2)$

Step 1

Expand $(2 i + 5) (i - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 i (i - 2) + 5 (i - 2)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$2 i i + 2 i \cdot - 2 + 5 i + 5 \cdot - 2$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2 i i$ .

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Step 2.1.1.1

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

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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

Step 2.1.1.4

Add $1$ and $1$ .

$2 i^{2} + 2 i \cdot - 2 + 5 i + 5 \cdot - 2$

Step 2.1.2

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

$2 \cdot - 1 + 2 i \cdot - 2 + 5 i + 5 \cdot - 2$

Step 2.1.3

Multiply $2$ by $- 1$ .

$- 2 + 2 i \cdot - 2 + 5 i + 5 \cdot - 2$

Step 2.1.4

Multiply $- 2$ by $2$ .

$- 2 - 4 i + 5 i + 5 \cdot - 2$

Step 2.1.5

Multiply $5$ by $- 2$ .

$- 2 - 4 i + 5 i - 10$

Step 2.2

Subtract $10$ from $- 2$ .

$- 12 - 4 i + 5 i$

Step 2.3

Add $- 4 i$ and $5 i$ .

$- 12 + i$