Question

perform the indicated operations and write the result in standard form.\\(\frac{-20 + sqrt{-75}}{40}\\)\\(\frac{-20 + sqrt{-75}}{40} = square\\)\\(\text{(type an exact answer, using radicals as needed. type your answer in the form } a + bi\text{.)}\\)

Explanation:

Step1: Simplify the imaginary radical

$\sqrt{-75} = \sqrt{25 \times (-3)} = 5\sqrt{3}i$

Step2: Substitute back into the expression

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

Step3: Split the fraction

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

Step4: Simplify each term

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

Answer:

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