Algebra Examples

{(1 - i)}^{2}

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

Step 1

Rewrite

{(1 - i)}^{2}

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

(1 - i) (1 - i)

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

(1 - i) (1 - i)

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

Step 2

Expand

(1 - i) (1 - i)

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

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Step 2.1

Apply the distributive property.

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

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

Step 2.2

Apply the distributive property.

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

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

Step 2.3

Apply the distributive property.

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

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

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.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

1

$1$ by

1

$1$ .

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

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

Step 3.1.2

Multiply

- i

$- i$ by

1

$1$ .

1 - i - i \cdot 1 - i (- i)

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

Step 3.1.3

Multiply

- 1

$- 1$ by

1

$1$ .

1 - i - i - i (- i)

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

Step 3.1.4

Multiply

- i (- i)

$- i (- i)$ .

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Step 3.1.4.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

1 - i - i + 1 i i

$1 - i - i + 1 i i$

Step 3.1.4.2

Raise

i

$i$ to the power of

1

$1$ .

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

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

Step 3.1.4.3

Raise

i

$i$ to the power of

1

$1$ .

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

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

Step 3.1.4.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 3.1.4.5

Add

1

$1$ and

1

$1$ .

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

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

Step 3.1.4.6

Multiply

i^{2}

$i^{2}$ by

1

$1$ .

1 - i - i + i^{2}

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

1 - i - i + i^{2}

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

Step 3.1.5

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

1 - i - i - 1

$1 - i - i - 1$

1 - i - i - 1

$1 - i - i - 1$

Step 3.2

Subtract

1

$1$ from

1

$1$ .

0 - i - i

$0 - i - i$

Step 3.3

Subtract

i

$i$ from

0

$0$ .

- i - i

$- i - i$

Step 3.4

Subtract

i

$i$ from

- i

$- i$ .

- 2 i

$- 2 i$

- 2 i

$- 2 i$

{(1 - i)}^{2}

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

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

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