Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $- 5$ by $- 2$ .

$10 - 5 (3 i) + 5 i \cdot - 2 + 5 i (3 i)$

Step 2.1.2

Multiply $3$ by $- 5$ .

$10 - 15 i + 5 i \cdot - 2 + 5 i (3 i)$

Step 2.1.3

Multiply $- 2$ by $5$ .

$10 - 15 i - 10 i + 5 i (3 i)$

Step 2.1.4

Multiply $5 i (3 i)$ .

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Step 2.1.4.1

Multiply $3$ by $5$ .

$10 - 15 i - 10 i + 15 i i$

Step 2.1.4.2

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

$10 - 15 i - 10 i + 15 (i^{1} i)$

Step 2.1.4.3

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

$10 - 15 i - 10 i + 15 (i^{1} i^{1})$

Step 2.1.4.4

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

$10 - 15 i - 10 i + 15 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$10 - 15 i - 10 i + 15 i^{2}$

Step 2.1.5

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

$10 - 15 i - 10 i + 15 \cdot - 1$

Step 2.1.6

Multiply $15$ by $- 1$ .

$10 - 15 i - 10 i - 15$

Step 2.2

Subtract $15$ from $10$ .

$- 5 - 15 i - 10 i$

Step 2.3

Subtract $10 i$ from $- 15 i$ .

$- 5 - 25 i$