Basic Math Examples

$(- 6 + i) (- 2 + 5 i)$

Step 1

Expand $(- 6 + i) (- 2 + 5 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 6 (- 2 + 5 i) + i (- 2 + 5 i)$

Step 1.2

Apply the distributive property.

$- 6 \cdot - 2 - 6 (5 i) + i (- 2 + 5 i)$

Step 1.3

Apply the distributive property.

$- 6 \cdot - 2 - 6 (5 i) + i \cdot - 2 + i (5 i)$

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 $- 6$ by $- 2$ .

$12 - 6 (5 i) + i \cdot - 2 + i (5 i)$

Step 2.1.2

Multiply $5$ by $- 6$ .

$12 - 30 i + i \cdot - 2 + i (5 i)$

Step 2.1.3

Move $- 2$ to the left of $i$ .

$12 - 30 i - 2 \cdot i + i (5 i)$

Step 2.1.4

Multiply $i (5 i)$ .

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Step 2.1.4.1

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

$12 - 30 i - 2 i + 5 (i^{1} i)$

Step 2.1.4.2

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

$12 - 30 i - 2 i + 5 (i^{1} i^{1})$

Step 2.1.4.3

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

$12 - 30 i - 2 i + 5 i^{1 + 1}$

Step 2.1.4.4

Add $1$ and $1$ .

$12 - 30 i - 2 i + 5 i^{2}$

Step 2.1.5

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

$12 - 30 i - 2 i + 5 \cdot - 1$

Step 2.1.6

Multiply $5$ by $- 1$ .

$12 - 30 i - 2 i - 5$

Step 2.2

Subtract $5$ from $12$ .

$7 - 30 i - 2 i$

Step 2.3

Subtract $2 i$ from $- 30 i$ .

$7 - 32 i$