Basic Math Examples

$(\frac{3}{4} + \frac{4}{5} \cdot i) - (\frac{1}{2} - \frac{3}{10} \cdot i)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{4}{5}$ and $i$ .

$\frac{3}{4} + \frac{4 i}{5} - (\frac{1}{2} - \frac{3}{10} \cdot i)$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine $i$ and $\frac{3}{10}$ .

$\frac{3}{4} + \frac{4 i}{5} - (\frac{1}{2} - \frac{i \cdot 3}{10})$

Step 1.2.2

Move $3$ to the left of $i$ .

$\frac{3}{4} + \frac{4 i}{5} - (\frac{1}{2} - \frac{3 i}{10})$

Step 1.3

Apply the distributive property.

$\frac{3}{4} + \frac{4 i}{5} - \frac{1}{2} - - \frac{3 i}{10}$

Step 1.4

Multiply $- - \frac{3 i}{10}$ .

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{3}{4} + \frac{4 i}{5} - \frac{1}{2} + 1 \frac{3 i}{10}$

Step 1.4.2

Multiply $\frac{3 i}{10}$ by $1$ .

$\frac{3}{4} + \frac{4 i}{5} - \frac{1}{2} + \frac{3 i}{10}$

Step 2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{4} - \frac{1}{2} \cdot \frac{2}{2} + \frac{4 i}{5} + \frac{3 i}{10}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{3}{4} - \frac{2}{2 \cdot 2} + \frac{4 i}{5} + \frac{3 i}{10}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{3}{4} - \frac{2}{4} + \frac{4 i}{5} + \frac{3 i}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 - 2}{4} + \frac{4 i}{5} + \frac{3 i}{10}$

Step 5

Subtract $2$ from $3$ .

$\frac{1}{4} + \frac{4 i}{5} + \frac{3 i}{10}$

Step 6

To write $\frac{4 i}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4} + \frac{4 i}{5} \cdot \frac{2}{2} + \frac{3 i}{10}$

Step 7

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{4 i}{5}$ by $\frac{2}{2}$ .

$\frac{1}{4} + \frac{4 i \cdot 2}{5 \cdot 2} + \frac{3 i}{10}$

Step 7.2

Multiply $5$ by $2$ .

$\frac{1}{4} + \frac{4 i \cdot 2}{10} + \frac{3 i}{10}$

Step 8

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{11 i}{10}$