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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $2$ .

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

Multiply $3$ by $7$ .

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

Multiply $2$ by $2$ .

$14 + 21 i + 4 i + 2 i (3 i)$

Multiply $2 i (3 i)$ .

Multiply $3$ by $2$ .

$14 + 21 i + 4 i + 6 i i$

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

$14 + 21 i + 4 i + 6 (i^{1} i)$

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

$14 + 21 i + 4 i + 6 (i^{1} i^{1})$

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

$14 + 21 i + 4 i + 6 i^{1 + 1}$

Add $1$ and $1$ .

$14 + 21 i + 4 i + 6 i^{2}$

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

$14 + 21 i + 4 i + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$14 + 21 i + 4 i - 6$

Subtract $6$ from $14$ .

$8 + 21 i + 4 i$

Add $21 i$ and $4 i$ .

$8 + 25 i$