Simplify (6+3i)(3+i)

$(6 + 3 i) (3 + i)$

Step 1

Expand $(6 + 3 i) (3 + i)$ using the FOIL Method.

Apply the distributive property.

$6 (3 + i) + 3 i (3 + i)$

Apply the distributive property.

$6 \cdot 3 + 6 i + 3 i (3 + i)$

Apply the distributive property.

$6 \cdot 3 + 6 i + 3 i \cdot 3 + 3 i i$

$6 \cdot 3 + 6 i + 3 i \cdot 3 + 3 i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $3$ .

$18 + 6 i + 3 i \cdot 3 + 3 i i$

Multiply $3$ by $3$ .

$18 + 6 i + 9 i + 3 i i$

Multiply $3 i i$ .

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

$18 + 6 i + 9 i + 3 (i^{1} i)$

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

$18 + 6 i + 9 i + 3 (i^{1} i^{1})$

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

$18 + 6 i + 9 i + 3 i^{1 + 1}$

Add $1$ and $1$ .

$18 + 6 i + 9 i + 3 i^{2}$

$18 + 6 i + 9 i + 3 i^{2}$

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

$18 + 6 i + 9 i + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$18 + 6 i + 9 i - 3$

$18 + 6 i + 9 i - 3$

Subtract $3$ from $18$ .

$15 + 6 i + 9 i$

Add $6 i$ and $9 i$ .

$15 + 15 i$

$15 + 15 i$

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