Simplify 3/4-2/3i+(1/8+5/6i)

$\frac{3}{4} - \frac{2}{3} \cdot i + (\frac{1}{8} + \frac{5}{6} \cdot i)$

Step 1

Remove parentheses.

$\frac{3}{4} - \frac{2}{3} \cdot i + \frac{1}{8} + \frac{5}{6} \cdot i$

Step 2

Simplify each term.

Combine $i$ and $\frac{2}{3}$ .

$\frac{3}{4} - \frac{i \cdot 2}{3} + \frac{1}{8} + \frac{5}{6} \cdot i$

Move $2$ to the left of $i$ .

$\frac{3}{4} - \frac{2 i}{3} + \frac{1}{8} + \frac{5}{6} \cdot i$

Combine $\frac{5}{6}$ and $i$ .

$\frac{3}{4} - \frac{2 i}{3} + \frac{1}{8} + \frac{5 i}{6}$

Step 3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{4} \cdot \frac{2}{2} + \frac{1}{8} - \frac{2 i}{3} + \frac{5 i}{6}$

Step 4

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 2}{4 \cdot 2} + \frac{1}{8} - \frac{2 i}{3} + \frac{5 i}{6}$

Multiply $4$ by $2$ .

$\frac{3 \cdot 2}{8} + \frac{1}{8} - \frac{2 i}{3} + \frac{5 i}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 1}{8} - \frac{2 i}{3} + \frac{5 i}{6}$

Step 6

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 + 1}{8} - \frac{2 i}{3} + \frac{5 i}{6}$

Add $6$ and $1$ .

$\frac{7}{8} - \frac{2 i}{3} + \frac{5 i}{6}$

Step 7

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

$\frac{7}{8} - \frac{2 i}{3} \cdot \frac{2}{2} + \frac{5 i}{6}$

Step 8

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

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

$\frac{7}{8} - \frac{2 i \cdot 2}{3 \cdot 2} + \frac{5 i}{6}$

Multiply $3$ by $2$ .

$\frac{7}{8} - \frac{2 i \cdot 2}{6} + \frac{5 i}{6}$

Step 9

Combine the numerators over the common denominator.

$\frac{7}{8} + \frac{i}{6}$

Simplify 3/4-2/3*i+(1/8+5/6*i)