Algebra Examples

$(3 - i) (\frac{3}{5} + \frac{1}{5} \cdot i)$

Step 1

Combine $\frac{1}{5}$ and $i$ .

$(3 - i) (\frac{3}{5} + \frac{i}{5})$

Step 2

Expand $(3 - i) (\frac{3}{5} + \frac{i}{5})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$3 (\frac{3}{5} + \frac{i}{5}) - i (\frac{3}{5} + \frac{i}{5})$

Step 2.2

Apply the distributive property.

$3 (\frac{3}{5}) + 3 \frac{i}{5} - i (\frac{3}{5} + \frac{i}{5})$

Step 2.3

Apply the distributive property.

$3 (\frac{3}{5}) + 3 \frac{i}{5} - i \frac{3}{5} - i \frac{i}{5}$

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 $3 (\frac{3}{5})$ .

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Step 3.1.1.1

Combine $3$ and $\frac{3}{5}$ .

$\frac{3 \cdot 3}{5} + 3 \frac{i}{5} - i \frac{3}{5} - i \frac{i}{5}$

Step 3.1.1.2

Multiply $3$ by $3$ .

$\frac{9}{5} + 3 \frac{i}{5} - i \frac{3}{5} - i \frac{i}{5}$

Step 3.1.2

Combine $3$ and $\frac{i}{5}$ .

$\frac{9}{5} + \frac{3 i}{5} - i \frac{3}{5} - i \frac{i}{5}$

Step 3.1.3

Combine $\frac{3}{5}$ and $i$ .

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - i \frac{i}{5}$

Step 3.1.4

Multiply $- i \frac{i}{5}$ .

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Step 3.1.4.1

Combine $\frac{i}{5}$ and $i$ .

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - \frac{i i}{5}$

Step 3.1.4.2

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

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - \frac{i^{1} i}{5}$

Step 3.1.4.3

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

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - \frac{i^{1} i^{1}}{5}$

Step 3.1.4.4

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

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - \frac{i^{1 + 1}}{5}$

Step 3.1.4.5

Add $1$ and $1$ .

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - \frac{i^{2}}{5}$

Step 3.1.5

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

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - \frac{- 1}{5}$

Step 3.1.6

Move the negative in front of the fraction.

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} - - \frac{1}{5}$

Step 3.1.7

Multiply $- - \frac{1}{5}$ .

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Step 3.1.7.1

Multiply $- 1$ by $- 1$ .

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} + 1 (\frac{1}{5})$

Step 3.1.7.2

Multiply $\frac{1}{5}$ by $1$ .

$\frac{9}{5} + \frac{3 i}{5} - \frac{3 i}{5} + \frac{1}{5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{9 + 1}{5} + \frac{3 i}{5} - \frac{3 i}{5}$

Step 3.3

Add $9$ and $1$ .

$\frac{10}{5} + \frac{3 i}{5} - \frac{3 i}{5}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{10}{5} + \frac{0}{5}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{10 + 0}{5}$

Step 3.6

Add $10$ and $0$ .

$\frac{10}{5}$

Step 4

Divide $10$ by $5$ .

$2$