Basic Math Examples

$(7 + i) (2 + 4 i)$

Step 1

Expand $(7 + i) (2 + 4 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 (2 + 4 i) + i (2 + 4 i)$

Step 1.2

Apply the distributive property.

$7 \cdot 2 + 7 (4 i) + i (2 + 4 i)$

Step 1.3

Apply the distributive property.

$7 \cdot 2 + 7 (4 i) + i \cdot 2 + i (4 i)$

$7 \cdot 2 + 7 (4 i) + i \cdot 2 + i (4 i)$

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 $2$ .

$14 + 7 (4 i) + i \cdot 2 + i (4 i)$

Step 2.1.2

Multiply $4$ by $7$ .

$14 + 28 i + i \cdot 2 + i (4 i)$

Step 2.1.3

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

$14 + 28 i + 2 \cdot i + i (4 i)$

Step 2.1.4

Multiply $i (4 i)$ .

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Step 2.1.4.1

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

$14 + 28 i + 2 i + 4 (i^{1} i)$

Step 2.1.4.2

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

$14 + 28 i + 2 i + 4 (i^{1} i^{1})$

Step 2.1.4.3

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

$14 + 28 i + 2 i + 4 i^{1 + 1}$

Step 2.1.4.4

Add $1$ and $1$ .

$14 + 28 i + 2 i + 4 i^{2}$

$14 + 28 i + 2 i + 4 i^{2}$

Step 2.1.5

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

$14 + 28 i + 2 i + 4 \cdot - 1$

Step 2.1.6

Multiply $4$ by $- 1$ .

$14 + 28 i + 2 i - 4$

$14 + 28 i + 2 i - 4$

Step 2.2

Subtract $4$ from $14$ .

$10 + 28 i + 2 i$

Step 2.3

Add $28 i$ and $2 i$ .

$10 + 30 i$

$10 + 30 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$