Simplify (7+i)(2+3i)

$(7 + i) (2 + 3 i)$

Step 1

Expand $(7 + i) (2 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$7 (2 + 3 i) + i (2 + 3 i)$

Apply the distributive property.

$7 \cdot 2 + 7 (3 i) + i (2 + 3 i)$

Apply the distributive property.

$7 \cdot 2 + 7 (3 i) + i \cdot 2 + i (3 i)$

$7 \cdot 2 + 7 (3 i) + i \cdot 2 + i (3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $2$ .

$14 + 7 (3 i) + i \cdot 2 + i (3 i)$

Multiply $3$ by $7$ .

$14 + 21 i + i \cdot 2 + i (3 i)$

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

$14 + 21 i + 2 \cdot i + i (3 i)$

Multiply $i (3 i)$ .

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

$14 + 21 i + 2 i + 3 (i^{1} i)$

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

$14 + 21 i + 2 i + 3 (i^{1} i^{1})$

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

$14 + 21 i + 2 i + 3 i^{1 + 1}$

Add $1$ and $1$ .

$14 + 21 i + 2 i + 3 i^{2}$

$14 + 21 i + 2 i + 3 i^{2}$

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

$14 + 21 i + 2 i + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$14 + 21 i + 2 i - 3$

$14 + 21 i + 2 i - 3$

Subtract $3$ from $14$ .

$11 + 21 i + 2 i$

Add $21 i$ and $2 i$ .

$11 + 23 i$

$11 + 23 i$

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