Simplify (1-i)^2

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

Step 1

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

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

Step 2

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 3

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 $- 1$ by $1$ .

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

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$1 - i - i + 1 i i$

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

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

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

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

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

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

Add $1$ and $1$ .

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

Multiply $i^{2}$ by $1$ .

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

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

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

$1 - i - i - 1$

$1 - i - i - 1$

Subtract $1$ from $1$ .

$0 - i - i$

Subtract $i$ from $0$ .

$- i - i$

Subtract $i$ from $- i$ .

$- 2 i$

$- 2 i$

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