Precalculus Examples

$\frac{5}{4} - (\frac{7}{4} + 2 i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{5}{4} - \frac{7}{4} - (2 i)$

Step 1.2

Multiply $2$ by $- 1$ .

$\frac{5}{4} - \frac{7}{4} - 2 i$

$\frac{5}{4} - \frac{7}{4} - 2 i$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$- 2 i + \frac{5 - 7}{4}$

Step 2.2

Subtract $7$ from $5$ .

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

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

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $- 2$ and $4$ .

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Step 3.1.1

Factor $2$ out of $- 2$ .

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $4$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$- 2 i + \frac{- 1}{2}$

$- 2 i + \frac{- 1}{2}$

$- 2 i + \frac{- 1}{2}$

Step 3.2

Move the negative in front of the fraction.

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

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

Step 4

Reorder $- 2 i$ and $- \frac{1}{2}$ .

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$