Trigonometry Examples

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

Step 1

Expand $(3 + 8 i) (4 - 6 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $3$ by $4$ .

$12 + 3 (- 6 i) + 8 i \cdot 4 + 8 i (- 6 i)$

Step 2.1.2

Multiply $- 6$ by $3$ .

$12 - 18 i + 8 i \cdot 4 + 8 i (- 6 i)$

Step 2.1.3

Multiply $4$ by $8$ .

$12 - 18 i + 32 i + 8 i (- 6 i)$

Step 2.1.4

Multiply $8 i (- 6 i)$ .

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Step 2.1.4.1

Multiply $- 6$ by $8$ .

$12 - 18 i + 32 i - 48 i i$

Step 2.1.4.2

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

$12 - 18 i + 32 i - 48 (i^{1} i)$

Step 2.1.4.3

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

$12 - 18 i + 32 i - 48 (i^{1} i^{1})$

Step 2.1.4.4

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

$12 - 18 i + 32 i - 48 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$12 - 18 i + 32 i - 48 i^{2}$

Step 2.1.5

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

$12 - 18 i + 32 i - 48 \cdot - 1$

Step 2.1.6

Multiply $- 48$ by $- 1$ .

$12 - 18 i + 32 i + 48$

Step 2.2

Add $12$ and $48$ .

$60 - 18 i + 32 i$

Step 2.3

Add $- 18 i$ and $32 i$ .

$60 + 14 i$