Precalculus Examples

$- (\frac{3}{2} + \frac{5}{2} \cdot i) + (\frac{5}{3} + \frac{11}{3} \cdot i)$

Step 1

Remove parentheses.

$- (\frac{3}{2} + \frac{5}{2} \cdot i) + \frac{5}{3} + \frac{11}{3} \cdot i$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

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

$- (\frac{3}{2} + \frac{5 i}{2}) + \frac{5}{3} + \frac{11}{3} \cdot i$

Step 2.2

Apply the distributive property.

$- \frac{3}{2} - \frac{5 i}{2} + \frac{5}{3} + \frac{11}{3} \cdot i$

Step 2.3

Combine $\frac{11}{3}$ and $i$ .

$- \frac{3}{2} - \frac{5 i}{2} + \frac{5}{3} + \frac{11 i}{3}$

Step 3

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{3}{2} \cdot \frac{3}{3} + \frac{5}{3} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 4

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3}{2} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{2}{2} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.1

Multiply $\frac{3}{2}$ by $\frac{3}{3}$ .

$- \frac{3 \cdot 3}{2 \cdot 3} + \frac{5}{3} \cdot \frac{2}{2} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 5.2

Multiply $2$ by $3$ .

$- \frac{3 \cdot 3}{6} + \frac{5}{3} \cdot \frac{2}{2} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 5.3

Multiply $\frac{5}{3}$ by $\frac{2}{2}$ .

$- \frac{3 \cdot 3}{6} + \frac{5 \cdot 2}{3 \cdot 2} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 5.4

Multiply $3$ by $2$ .

$- \frac{3 \cdot 3}{6} + \frac{5 \cdot 2}{6} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 3 + 5 \cdot 2}{6} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply $- 3$ by $3$ .

$\frac{- 9 + 5 \cdot 2}{6} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 7.2

Multiply $5$ by $2$ .

$\frac{- 9 + 10}{6} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 7.3

Add $- 9$ and $10$ .

$\frac{1}{6} - \frac{5 i}{2} + \frac{11 i}{3}$

Step 8

To write $- \frac{5 i}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{6} - \frac{5 i}{2} \cdot \frac{3}{3} + \frac{11 i}{3}$

Step 9

To write $\frac{11 i}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{6} - \frac{5 i}{2} \cdot \frac{3}{3} + \frac{11 i}{3} \cdot \frac{2}{2}$

Step 10

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 10.1

Multiply $\frac{5 i}{2}$ by $\frac{3}{3}$ .

$\frac{1}{6} - \frac{5 i \cdot 3}{2 \cdot 3} + \frac{11 i}{3} \cdot \frac{2}{2}$

Step 10.2

Multiply $2$ by $3$ .

$\frac{1}{6} - \frac{5 i \cdot 3}{6} + \frac{11 i}{3} \cdot \frac{2}{2}$

Step 10.3

Multiply $\frac{11 i}{3}$ by $\frac{2}{2}$ .

$\frac{1}{6} - \frac{5 i \cdot 3}{6} + \frac{11 i \cdot 2}{3 \cdot 2}$

Step 10.4

Multiply $3$ by $2$ .

$\frac{1}{6} - \frac{5 i \cdot 3}{6} + \frac{11 i \cdot 2}{6}$

Step 11

Combine the numerators over the common denominator.

$\frac{1}{6} + \frac{7 i}{6}$