Simplify (x-i)(x+i)

$(x - i) (x + i)$

Step 1

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

Apply the distributive property.

$x (x + i) - i (x + i)$

Apply the distributive property.

$x \cdot x + x i - i (x + i)$

Apply the distributive property.

$x \cdot x + x i - i x - i i$

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x i - i x - i i$ .

Reorder the factors in the terms $x i$ and $- i x$ .

$x \cdot x + i x - i x - i i$

Subtract $i x$ from $i x$ .

$x \cdot x + 0 - i i$

Add $x \cdot x$ and $0$ .

$x \cdot x - i i$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - i i$

Multiply $- i i$ .

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

$x^{2} - (i^{1} i)$

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

$x^{2} - (i^{1} i^{1})$

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

$x^{2} - i^{1 + 1}$

Add $1$ and $1$ .

$x^{2} - i^{2}$

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

$x^{2} - - 1$

Multiply $- 1$ by $- 1$ .

$x^{2} + 1$