Basic Math Examples

$(7 + i) (- 4 + 3 i)$

Step 1

Expand $(7 + i) (- 4 + 3 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 (- 4 + 3 i) + i (- 4 + 3 i)$

Step 1.2

Apply the distributive property.

$7 \cdot - 4 + 7 (3 i) + i (- 4 + 3 i)$

Step 1.3

Apply the distributive property.

$7 \cdot - 4 + 7 (3 i) + i \cdot - 4 + i (3 i)$

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 $7$ by $- 4$ .

$- 28 + 7 (3 i) + i \cdot - 4 + i (3 i)$

Step 2.1.2

Multiply $3$ by $7$ .

$- 28 + 21 i + i \cdot - 4 + i (3 i)$

Step 2.1.3

Move $- 4$ to the left of $i$ .

$- 28 + 21 i - 4 \cdot i + i (3 i)$

Step 2.1.4

Multiply $i (3 i)$ .

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Step 2.1.4.1

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

$- 28 + 21 i - 4 i + 3 (i^{1} i)$

Step 2.1.4.2

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

$- 28 + 21 i - 4 i + 3 (i^{1} i^{1})$

Step 2.1.4.3

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

$- 28 + 21 i - 4 i + 3 i^{1 + 1}$

Step 2.1.4.4

Add $1$ and $1$ .

$- 28 + 21 i - 4 i + 3 i^{2}$

Step 2.1.5

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

$- 28 + 21 i - 4 i + 3 \cdot - 1$

Step 2.1.6

Multiply $3$ by $- 1$ .

$- 28 + 21 i - 4 i - 3$

Step 2.2

Subtract $3$ from $- 28$ .

$- 31 + 21 i - 4 i$

Step 2.3

Subtract $4 i$ from $21 i$ .

$- 31 + 17 i$