Precalculus Examples

$(- 1 + 6 i) (5 + i)$

Step 1

Expand $(- 1 + 6 i) (5 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 1 (5 + i) + 6 i (5 + i)$

Step 1.2

Apply the distributive property.

$- 1 \cdot 5 - 1 i + 6 i (5 + i)$

Step 1.3

Apply the distributive property.

$- 1 \cdot 5 - 1 i + 6 i \cdot 5 + 6 i i$

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 $- 1$ by $5$ .

$- 5 - 1 i + 6 i \cdot 5 + 6 i i$

Step 2.1.2

Rewrite $- 1 i$ as $- i$ .

$- 5 - i + 6 i \cdot 5 + 6 i i$

Step 2.1.3

Multiply $5$ by $6$ .

$- 5 - i + 30 i + 6 i i$

Step 2.1.4

Multiply $6 i i$ .

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Step 2.1.4.1

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

$- 5 - i + 30 i + 6 (i^{1} i)$

Step 2.1.4.2

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

$- 5 - i + 30 i + 6 (i^{1} i^{1})$

Step 2.1.4.3

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

$- 5 - i + 30 i + 6 i^{1 + 1}$

Step 2.1.4.4

Add $1$ and $1$ .

$- 5 - i + 30 i + 6 i^{2}$

Step 2.1.5

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

$- 5 - i + 30 i + 6 \cdot - 1$

Step 2.1.6

Multiply $6$ by $- 1$ .

$- 5 - i + 30 i - 6$

Step 2.2

Subtract $6$ from $- 5$ .

$- 11 - i + 30 i$

Step 2.3

Add $- i$ and $30 i$ .

$- 11 + 29 i$