Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 1$ by $2$ .

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

Step 2.1.2

Multiply $- 1$ by $- 1$ .

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

Step 2.1.3

Multiply $i$ by $1$ .

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

Step 2.1.4

Move $2$ to the left of $i$ .

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

Step 2.1.5

Multiply $i (- i)$ .

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Step 2.1.5.1

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

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

Step 2.1.5.2

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

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

Step 2.1.5.3

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

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

Step 2.1.5.4

Add $1$ and $1$ .

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

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

Step 2.1.6

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

$- 2 + i + 2 i - - 1$

Step 2.1.7

Multiply $- 1$ by $- 1$ .

$- 2 + i + 2 i + 1$

$- 2 + i + 2 i + 1$

Step 2.2

Add $- 2$ and $1$ .

$- 1 + i + 2 i$

Step 2.3

Add $i$ and $2 i$ .

$- 1 + 3 i$

$- 1 + 3 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$