Simplify (1-i)(i-2)

$(1 - i) (i - 2)$

Step 1

Expand $(1 - i) (i - 2)$ using the FOIL Method.

Apply the distributive property.

$1 (i - 2) - i (i - 2)$

Apply the distributive property.

$1 i + 1 \cdot - 2 - i (i - 2)$

Apply the distributive property.

$1 i + 1 \cdot - 2 - i i - i \cdot - 2$

$1 i + 1 \cdot - 2 - i i - i \cdot - 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $i$ by $1$ .

$i + 1 \cdot - 2 - i i - i \cdot - 2$

Multiply $- 2$ by $1$ .

$i - 2 - i i - i \cdot - 2$

Multiply $- i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

$i - 2 - i^{2} - i \cdot - 2$

$i - 2 - i^{2} - i \cdot - 2$

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

$i - 2 - - 1 - i \cdot - 2$

Multiply $- 1$ by $- 1$ .

$i - 2 + 1 - i \cdot - 2$

Multiply $- 2$ by $- 1$ .

$i - 2 + 1 + 2 i$

$i - 2 + 1 + 2 i$

Add $i$ and $2 i$ .

$- 2 + 1 + 3 i$

Add $- 2$ and $1$ .

$- 1 + 3 i$

$- 1 + 3 i$

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