Simplify (2-i)/5(i+2)

$\frac{2 - i}{5} (i + 2)$

Split the fraction $\frac{2 - i}{5}$ into two fractions.

$(\frac{2}{5} + \frac{- i}{5}) \cdot (i + 2)$

Move the negative in front of the fraction.

$(\frac{2}{5} - \frac{i}{5}) \cdot (i + 2)$

Expand $(\frac{2}{5} - \frac{i}{5}) (i + 2)$ using the FOIL Method.

Apply the distributive property.

$\frac{2}{5} (i + 2) - \frac{i}{5} (i + 2)$

Apply the distributive property.

$\frac{2}{5} i + \frac{2}{5} \cdot 2 - \frac{i}{5} (i + 2)$

Apply the distributive property.

$\frac{2}{5} i + \frac{2}{5} \cdot 2 - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Simplify and combine like terms.

Simplify each term.

Combine $\frac{2}{5}$ and $i$ .

$\frac{2 i}{5} + \frac{2}{5} \cdot 2 - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Multiply $\frac{2}{5} \cdot 2$ .

Combine $\frac{2}{5}$ and $2$ .

$\frac{2 i}{5} + \frac{2 \cdot 2}{5} - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Multiply $2$ by $2$ .

$\frac{2 i}{5} + \frac{4}{5} - \frac{i}{5} i - \frac{i}{5} \cdot 2$

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

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i i}{5} - \frac{i}{5} \cdot 2$

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{1} i}{5} - \frac{i}{5} \cdot 2$

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{1} i^{1}}{5} - \frac{i}{5} \cdot 2$

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{1 + 1}}{5} - \frac{i}{5} \cdot 2$

Add $1$ and $1$ .

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{2}}{5} - \frac{i}{5} \cdot 2$

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{- 1}{5} - \frac{i}{5} \cdot 2$

Move the negative in front of the fraction.

$\frac{2 i}{5} + \frac{4}{5} - - \frac{1}{5} - \frac{i}{5} \cdot 2$

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

Multiply $- 1$ by $- 1$ .

$\frac{2 i}{5} + \frac{4}{5} + 1 (\frac{1}{5}) - \frac{i}{5} \cdot 2$

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

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} - \frac{i}{5} \cdot 2$

Multiply $- \frac{i}{5} \cdot 2$ .

Multiply $2$ by $- 1$ .

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} - 2 \frac{i}{5}$

Combine $- 2$ and $\frac{i}{5}$ .

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} + \frac{- 2 i}{5}$

Move the negative in front of the fraction.

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} - \frac{2 i}{5}$

Combine the numerators over the common denominator.

$\frac{0}{5} + \frac{4}{5} + \frac{1}{5}$

Combine the numerators over the common denominator.

$\frac{0 + 4}{5} + \frac{1}{5}$

Add $0$ and $4$ .

$\frac{4}{5} + \frac{1}{5}$

Combine the numerators over the common denominator.

$\frac{4 + 1}{5}$

Add $4$ and $1$ .

$\frac{5}{5}$

Divide $5$ by $5$ .

$1$

Simplify (2-i)/5(i+2)

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