Simplify (5+6i)(5-6i)

$(5 + 6 i) (5 - 6 i)$

Step 1

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

Apply the distributive property.

$5 (5 - 6 i) + 6 i (5 - 6 i)$

Apply the distributive property.

$5 \cdot 5 + 5 (- 6 i) + 6 i (5 - 6 i)$

Apply the distributive property.

$5 \cdot 5 + 5 (- 6 i) + 6 i \cdot 5 + 6 i (- 6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

$25 + 5 (- 6 i) + 6 i \cdot 5 + 6 i (- 6 i)$

Multiply $- 6$ by $5$ .

$25 - 30 i + 6 i \cdot 5 + 6 i (- 6 i)$

Multiply $5$ by $6$ .

$25 - 30 i + 30 i + 6 i (- 6 i)$

Multiply $6 i (- 6 i)$ .

Multiply $- 6$ by $6$ .

$25 - 30 i + 30 i - 36 i i$

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

$25 - 30 i + 30 i - 36 (i^{1} i)$

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

$25 - 30 i + 30 i - 36 (i^{1} i^{1})$

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

$25 - 30 i + 30 i - 36 i^{1 + 1}$

Add $1$ and $1$ .

$25 - 30 i + 30 i - 36 i^{2}$

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

$25 - 30 i + 30 i - 36 \cdot - 1$

Multiply $- 36$ by $- 1$ .

$25 - 30 i + 30 i + 36$

Add $25$ and $36$ .

$61 - 30 i + 30 i$

Add $- 30 i$ and $30 i$ .

$61 + 0$

Add $61$ and $0$ .

$61$