Simplify (8+3i)(8-3i)

$(8 + 3 i) (8 - 3 i)$

Step 1

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

Apply the distributive property.

$8 (8 - 3 i) + 3 i (8 - 3 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 3 i) + 3 i (8 - 3 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 3 i) + 3 i \cdot 8 + 3 i (- 3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$64 + 8 (- 3 i) + 3 i \cdot 8 + 3 i (- 3 i)$

Multiply $- 3$ by $8$ .

$64 - 24 i + 3 i \cdot 8 + 3 i (- 3 i)$

Multiply $8$ by $3$ .

$64 - 24 i + 24 i + 3 i (- 3 i)$

Multiply $3 i (- 3 i)$ .

Multiply $- 3$ by $3$ .

$64 - 24 i + 24 i - 9 i i$

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

$64 - 24 i + 24 i - 9 (i^{1} i)$

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

$64 - 24 i + 24 i - 9 (i^{1} i^{1})$

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

$64 - 24 i + 24 i - 9 i^{1 + 1}$

Add $1$ and $1$ .

$64 - 24 i + 24 i - 9 i^{2}$

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

$64 - 24 i + 24 i - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$64 - 24 i + 24 i + 9$

Add $64$ and $9$ .

$73 - 24 i + 24 i$

Add $- 24 i$ and $24 i$ .

$73 + 0$

Add $73$ and $0$ .

$73$