Simplify (4+6i)(4-6i)

$(4 + 6 i) (4 - 6 i)$

Step 1

Expand $(4 + 6 i) (4 - 6 i)$ using the FOIL Method.

Apply the distributive property.

$4 (4 - 6 i) + 6 i (4 - 6 i)$

Apply the distributive property.

$4 \cdot 4 + 4 (- 6 i) + 6 i (4 - 6 i)$

Apply the distributive property.

$4 \cdot 4 + 4 (- 6 i) + 6 i \cdot 4 + 6 i (- 6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- 6 i) + 6 i \cdot 4 + 6 i (- 6 i)$

Multiply $- 6$ by $4$ .

$16 - 24 i + 6 i \cdot 4 + 6 i (- 6 i)$

Multiply $4$ by $6$ .

$16 - 24 i + 24 i + 6 i (- 6 i)$

Multiply $6 i (- 6 i)$ .

Multiply $- 6$ by $6$ .

$16 - 24 i + 24 i - 36 i i$

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

$16 - 24 i + 24 i - 36 (i^{1} i)$

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

$16 - 24 i + 24 i - 36 (i^{1} i^{1})$

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

$16 - 24 i + 24 i - 36 i^{1 + 1}$

Add $1$ and $1$ .

$16 - 24 i + 24 i - 36 i^{2}$

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

$16 - 24 i + 24 i - 36 \cdot - 1$

Multiply $- 36$ by $- 1$ .

$16 - 24 i + 24 i + 36$

Add $16$ and $36$ .

$52 - 24 i + 24 i$

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

$52 + 0$

Add $52$ and $0$ .

$52$