Trigonometry Examples

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

Step 1

Expand $(- 2 + 6 i) (3 + 4 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $- 2$ by $3$ .

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

Step 2.1.2

Multiply $4$ by $- 2$ .

$- 6 - 8 i + 6 i \cdot 3 + 6 i (4 i)$

Step 2.1.3

Multiply $3$ by $6$ .

$- 6 - 8 i + 18 i + 6 i (4 i)$

Step 2.1.4

Multiply $6 i (4 i)$ .

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Step 2.1.4.1

Multiply $4$ by $6$ .

$- 6 - 8 i + 18 i + 24 i i$

Step 2.1.4.2

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

$- 6 - 8 i + 18 i + 24 (i^{1} i)$

Step 2.1.4.3

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

$- 6 - 8 i + 18 i + 24 (i^{1} i^{1})$

Step 2.1.4.4

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

$- 6 - 8 i + 18 i + 24 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$- 6 - 8 i + 18 i + 24 i^{2}$

Step 2.1.5

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

$- 6 - 8 i + 18 i + 24 \cdot - 1$

Step 2.1.6

Multiply $24$ by $- 1$ .

$- 6 - 8 i + 18 i - 24$

Step 2.2

Subtract $24$ from $- 6$ .

$- 30 - 8 i + 18 i$

Step 2.3

Add $- 8 i$ and $18 i$ .

$- 30 + 10 i$