Write in Standard Form -(20-i square root of 75)/40

$- \frac{20 - i \sqrt{75}}{40}$

Step 1

Simplify the numerator.

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$- \frac{20 - i \sqrt{25 (3)}}{40}$

Rewrite $25$ as $5^{2}$ .

$- \frac{20 - i \sqrt{5^{2} \cdot 3}}{40}$

Pull terms out from under the radical.

$- \frac{20 - i (5 \sqrt{3})}{40}$

Multiply $5$ by $- 1$ .

$- \frac{20 - 5 i \sqrt{3}}{40}$

Step 2

Cancel the common factor of $20 - 5 i \sqrt{3}$ and $40$ .

Factor $5$ out of $20$ .

$- \frac{5 (4) - 5 i \sqrt{3}}{40}$

Factor $5$ out of $- 5 i \sqrt{3}$ .

$- \frac{5 (4) + 5 (- i \sqrt{3})}{40}$

Factor $5$ out of $5 (4) + 5 (- i \sqrt{3})$ .

$- \frac{5 (4 - i \sqrt{3})}{40}$

Cancel the common factors.

Factor $5$ out of $40$ .

$- \frac{5 (4 - i \sqrt{3})}{5 \cdot 8}$

Cancel the common factor.

$- \frac{5 (4 - i \sqrt{3})}{5 \cdot 8}$

Rewrite the expression.

$- \frac{4 - i \sqrt{3}}{8}$

Step 3

Split the fraction $\frac{4 - i \sqrt{3}}{8}$ into two fractions.

$- (\frac{4}{8} + \frac{- i \sqrt{3}}{8})$

Step 4

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$- (\frac{4 (1)}{8} + \frac{- i \sqrt{3}}{8})$

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- (\frac{1}{2} + \frac{- i \sqrt{3}}{8})$

Step 5

Move the negative in front of the fraction.

$- (\frac{1}{2} - \frac{i \sqrt{3}}{8})$