Precalculus Examples

$(3 - 4 i) (5 - 12 i)$

Step 1

Expand $(3 - 4 i) (5 - 12 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (5 - 12 i) - 4 i (5 - 12 i)$

Step 1.2

Apply the distributive property.

$3 \cdot 5 + 3 (- 12 i) - 4 i (5 - 12 i)$

Step 1.3

Apply the distributive property.

$3 \cdot 5 + 3 (- 12 i) - 4 i \cdot 5 - 4 i (- 12 i)$

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 $5$ .

$15 + 3 (- 12 i) - 4 i \cdot 5 - 4 i (- 12 i)$

Step 2.1.2

Multiply $- 12$ by $3$ .

$15 - 36 i - 4 i \cdot 5 - 4 i (- 12 i)$

Step 2.1.3

Multiply $5$ by $- 4$ .

$15 - 36 i - 20 i - 4 i (- 12 i)$

Step 2.1.4

Multiply $- 4 i (- 12 i)$ .

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Step 2.1.4.1

Multiply $- 12$ by $- 4$ .

$15 - 36 i - 20 i + 48 i i$

Step 2.1.4.2

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

$15 - 36 i - 20 i + 48 (i^{1} i)$

Step 2.1.4.3

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

$15 - 36 i - 20 i + 48 (i^{1} i^{1})$

Step 2.1.4.4

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

$15 - 36 i - 20 i + 48 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$15 - 36 i - 20 i + 48 i^{2}$

Step 2.1.5

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

$15 - 36 i - 20 i + 48 \cdot - 1$

Step 2.1.6

Multiply $48$ by $- 1$ .

$15 - 36 i - 20 i - 48$

Step 2.2

Subtract $48$ from $15$ .

$- 33 - 36 i - 20 i$

Step 2.3

Subtract $20 i$ from $- 36 i$ .

$- 33 - 56 i$