Simplify (8+5i)(6+3i)

$(8 + 5 i) (6 + 3 i)$

Step 1

Expand $(8 + 5 i) (6 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$8 (6 + 3 i) + 5 i (6 + 3 i)$

Apply the distributive property.

$8 \cdot 6 + 8 (3 i) + 5 i (6 + 3 i)$

Apply the distributive property.

$8 \cdot 6 + 8 (3 i) + 5 i \cdot 6 + 5 i (3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $6$ .

$48 + 8 (3 i) + 5 i \cdot 6 + 5 i (3 i)$

Multiply $3$ by $8$ .

$48 + 24 i + 5 i \cdot 6 + 5 i (3 i)$

Multiply $6$ by $5$ .

$48 + 24 i + 30 i + 5 i (3 i)$

Multiply $5 i (3 i)$ .

Multiply $3$ by $5$ .

$48 + 24 i + 30 i + 15 i i$

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

$48 + 24 i + 30 i + 15 (i^{1} i)$

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

$48 + 24 i + 30 i + 15 (i^{1} i^{1})$

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

$48 + 24 i + 30 i + 15 i^{1 + 1}$

Add $1$ and $1$ .

$48 + 24 i + 30 i + 15 i^{2}$

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

$48 + 24 i + 30 i + 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$48 + 24 i + 30 i - 15$

Subtract $15$ from $48$ .

$33 + 24 i + 30 i$

Add $24 i$ and $30 i$ .

$33 + 54 i$