Simplify (1+i)(1-i)

$(1 + i) (1 - i)$

Step 1

Expand $(1 + i) (1 - i)$ using the FOIL Method.

Apply the distributive property.

$1 (1 - i) + i (1 - i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- i) + i (1 - i)$

Apply the distributive property.

$1 \cdot 1 + 1 (- i) + i \cdot 1 + i (- i)$

$1 \cdot 1 + 1 (- i) + i \cdot 1 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 (- i) + i \cdot 1 + i (- i)$

Multiply $- i$ by $1$ .

$1 - i + i \cdot 1 + i (- i)$

Multiply $i$ by $1$ .

$1 - i + i + i (- i)$

Multiply $i (- i)$ .

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

$1 - i + i - (i^{1} i)$

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

$1 - i + i - (i^{1} i^{1})$

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

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

Add $1$ and $1$ .

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

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

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

$1 - i + i - - 1$

Multiply $- 1$ by $- 1$ .

$1 - i + i + 1$

$1 - i + i + 1$

Add $1$ and $1$ .

$2 - i + i$

Add $- i$ and $i$ .

$2 + 0$

Add $2$ and $0$ .

$2$

$2$

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