Simplify (2+5i)(2-5i)

$(2 + 5 i) (2 - 5 i)$

Step 1

Expand $(2 + 5 i) (2 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$2 (2 - 5 i) + 5 i (2 - 5 i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- 5 i) + 5 i (2 - 5 i)$

Apply the distributive property.

$2 \cdot 2 + 2 (- 5 i) + 5 i \cdot 2 + 5 i (- 5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- 5 i) + 5 i \cdot 2 + 5 i (- 5 i)$

Multiply $- 5$ by $2$ .

$4 - 10 i + 5 i \cdot 2 + 5 i (- 5 i)$

Multiply $2$ by $5$ .

$4 - 10 i + 10 i + 5 i (- 5 i)$

Multiply $5 i (- 5 i)$ .

Multiply $- 5$ by $5$ .

$4 - 10 i + 10 i - 25 i i$

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

$4 - 10 i + 10 i - 25 (i^{1} i)$

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

$4 - 10 i + 10 i - 25 (i^{1} i^{1})$

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

$4 - 10 i + 10 i - 25 i^{1 + 1}$

Add $1$ and $1$ .

$4 - 10 i + 10 i - 25 i^{2}$

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

$4 - 10 i + 10 i - 25 \cdot - 1$

Multiply $- 25$ by $- 1$ .

$4 - 10 i + 10 i + 25$

Add $4$ and $25$ .

$29 - 10 i + 10 i$

Add $- 10 i$ and $10 i$ .

$29 + 0$

Add $29$ and $0$ .

$29$