Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite ${(- 1)}^{\frac{3}{2}}$ as $\sqrt{{(- 1)}^{3}}$ .

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

Step 1.1.2

Raise $- 1$ to the power of $3$ .

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

Step 1.1.3

Rewrite $\sqrt{- 1}$ as $i$ .

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

Step 1.2

Move the negative in front of the fraction.

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

Step 1.3

Multiply $4$ by $- 1$ .

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

Step 1.4

Raise $- 1$ to the power of $2$ .

$- \frac{3 i}{2} - 4 - \frac{1}{2}$

Step 2

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

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

Step 3

Combine $- 4$ and $\frac{2}{2}$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{- 8 - 3 i}{2} - \frac{1}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 8 - 3 i - 1}{2}$

Step 6

Subtract $1$ from $- 8$ .

$\frac{- 9 - 3 i}{2}$

Step 7

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- 1 (9) - 3 i}{2}$

Step 8

Factor $- 1$ out of $- 3 i$ .

$\frac{- 1 (9) - (3 i)}{2}$

Step 9

Factor $- 1$ out of $- 1 (9) - (3 i)$ .

$\frac{- 1 (9 + 3 i)}{2}$

Step 10

Move the negative in front of the fraction.

$- \frac{9 + 3 i}{2}$