Algebra Examples

(3 - 2 i) (5 + i)

$(3 - 2 i) (5 + i)$

Step 1

Expand

(3 - 2 i) (5 + i)

$(3 - 2 i) (5 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

3 (5 + i) - 2 i (5 + i)

$3 (5 + i) - 2 i (5 + i)$

Step 1.2

Apply the distributive property.

3 \cdot 5 + 3 i - 2 i (5 + i)

$3 \cdot 5 + 3 i - 2 i (5 + i)$

Step 1.3

Apply the distributive property.

3 \cdot 5 + 3 i - 2 i \cdot 5 - 2 i i

$3 \cdot 5 + 3 i - 2 i \cdot 5 - 2 i i$

3 \cdot 5 + 3 i - 2 i \cdot 5 - 2 i i

$3 \cdot 5 + 3 i - 2 i \cdot 5 - 2 i i$

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

3

$3$ by

5

$5$ .

15 + 3 i - 2 i \cdot 5 - 2 i i

$15 + 3 i - 2 i \cdot 5 - 2 i i$

Step 2.1.2

Multiply

5

$5$ by

- 2

$- 2$ .

15 + 3 i - 10 i - 2 i i

$15 + 3 i - 10 i - 2 i i$

Step 2.1.3

Multiply

- 2 i i

$- 2 i i$ .

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Step 2.1.3.1

Raise

i

$i$ to the power of

1

$1$ .

15 + 3 i - 10 i - 2 (i^{1} i)

$15 + 3 i - 10 i - 2 (i^{1} i)$

Step 2.1.3.2

Raise

i

$i$ to the power of

1

$1$ .

15 + 3 i - 10 i - 2 (i^{1} i^{1})

$15 + 3 i - 10 i - 2 (i^{1} i^{1})$

Step 2.1.3.3

Use the power rule

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

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

15 + 3 i - 10 i - 2 i^{1 + 1}

$15 + 3 i - 10 i - 2 i^{1 + 1}$

Step 2.1.3.4

Add

1

$1$ and

1

$1$ .

15 + 3 i - 10 i - 2 i^{2}

$15 + 3 i - 10 i - 2 i^{2}$

15 + 3 i - 10 i - 2 i^{2}

$15 + 3 i - 10 i - 2 i^{2}$

Step 2.1.4

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

15 + 3 i - 10 i - 2 \cdot - 1

$15 + 3 i - 10 i - 2 \cdot - 1$

Step 2.1.5

Multiply

- 2

$- 2$ by

- 1

$- 1$ .

15 + 3 i - 10 i + 2

$15 + 3 i - 10 i + 2$

15 + 3 i - 10 i + 2

$15 + 3 i - 10 i + 2$

Step 2.2

Add

15

$15$ and

2

$2$ .

17 + 3 i - 10 i

$17 + 3 i - 10 i$

Step 2.3

Subtract

10 i

$10 i$ from

3 i

$3 i$ .

17 - 7 i

$17 - 7 i$

17 - 7 i

$17 - 7 i$

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

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