Basic Math Examples

$(3 + 6 i) (- 2 + 5 i)$

Step 1

Expand $(3 + 6 i) (- 2 + 5 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (- 2 + 5 i) + 6 i (- 2 + 5 i)$

Step 1.2

Apply the distributive property.

$3 \cdot - 2 + 3 (5 i) + 6 i (- 2 + 5 i)$

Step 1.3

Apply the distributive property.

$3 \cdot - 2 + 3 (5 i) + 6 i \cdot - 2 + 6 i (5 i)$

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 $3$ by $- 2$ .

$- 6 + 3 (5 i) + 6 i \cdot - 2 + 6 i (5 i)$

Step 2.1.2

Multiply $5$ by $3$ .

$- 6 + 15 i + 6 i \cdot - 2 + 6 i (5 i)$

Step 2.1.3

Multiply $- 2$ by $6$ .

$- 6 + 15 i - 12 i + 6 i (5 i)$

Step 2.1.4

Multiply $6 i (5 i)$ .

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Step 2.1.4.1

Multiply $5$ by $6$ .

$- 6 + 15 i - 12 i + 30 i i$

Step 2.1.4.2

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

$- 6 + 15 i - 12 i + 30 (i^{1} i)$

Step 2.1.4.3

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

$- 6 + 15 i - 12 i + 30 (i^{1} i^{1})$

Step 2.1.4.4

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

$- 6 + 15 i - 12 i + 30 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$- 6 + 15 i - 12 i + 30 i^{2}$

Step 2.1.5

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

$- 6 + 15 i - 12 i + 30 \cdot - 1$

Step 2.1.6

Multiply $30$ by $- 1$ .

$- 6 + 15 i - 12 i - 30$

Step 2.2

Subtract $30$ from $- 6$ .

$- 36 + 15 i - 12 i$

Step 2.3

Subtract $12 i$ from $15 i$ .

$- 36 + 3 i$