Simplify (3/4+4/5i)-(1/2-3/10i)

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

Step 1

Simplify each term.

Combine

$\frac{4}{5}$ and

$i$ .

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

Simplify each term.

Combine

$i$ and

$\frac{3}{10}$ .

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

Move

$3$ to the left of

$i$ .

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

Apply the distributive property.

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

Multiply

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

Multiply

$- 1$ by

$- 1$ .

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

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

$1$ .

Multiply

$\frac{1}{2}$ by

$\frac{2}{2}$ .

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

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

$1$ .

Multiply

$\frac{4 i}{5}$ by

$\frac{2}{2}$ .

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

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.

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

Simplify (3/4+4/5*i)-(1/2-3/10*i)

Related Questions

Simplify (3/4+4/5i)-(1/2-3/10i)