Algebra Examples

$- 3 i + (\frac{3}{4} + 2 i) - (\frac{9}{3} + 3 i)$

Step 1

Simplify each term.

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Step 1.1

Divide $9$ by $3$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $- 1$ by $3$ .

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

Step 1.4

Multiply $3$ by $- 1$ .

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

Step 2

Add $- 3 i$ and $2 i$ .

$\frac{3}{4} - i - 3 - 3 i$

Step 3

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

$\frac{3}{4} - 3 \cdot \frac{4}{4} - i - 3 i$

Step 4

Combine $- 3$ and $\frac{4}{4}$ .

$\frac{3}{4} + \frac{- 3 \cdot 4}{4} - i - 3 i$

Step 5

Combine the numerators over the common denominator.

$\frac{3 - 3 \cdot 4}{4} - i - 3 i$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $4$ .

$\frac{3 - 12}{4} - i - 3 i$

Step 6.2

Subtract $12$ from $3$ .

$\frac{- 9}{4} - i - 3 i$

Step 7

Move the negative in front of the fraction.

$- \frac{9}{4} - i - 3 i$

Step 8

Subtract $3 i$ from $- i$ .

$- \frac{9}{4} - 4 i$