Questions: -4 + √(-8) / 6

Transcript text: $\frac{-4+\sqrt{-8}}{6}$

Solution

Solution Steps

To solve the expression $\frac{-4+\sqrt{-8}}{6}$, we need to handle the square root of a negative number, which involves complex numbers. We will use Python's complex number support to compute the result.

Step 1: Calculate the Square Root

We start with the expression $\sqrt{-8}$. Since $-8$ is negative, we can express it in terms of imaginary numbers: \[ \sqrt{-8} = \sqrt{8} \cdot i = 2\sqrt{2} \cdot i \]

Step 2: Substitute and Simplify the Numerator

Now we substitute $\sqrt{-8}$ back into the expression: \[ -4 + \sqrt{-8} = -4 + 2\sqrt{2}i \]

Step 3: Divide by the Denominator

Next, we divide the entire numerator by $6$: \[ \frac{-4 + 2\sqrt{2}i}{6} = \frac{-4}{6} + \frac{2\sqrt{2}i}{6} = -\frac{2}{3} + \frac{\sqrt{2}}{3}i \]

Final Answer

Thus, the final result of the expression $\frac{-4+\sqrt{-8}}{6}$ is: \[ \boxed{-\frac{2}{3} + \frac{\sqrt{2}}{3}i} \]

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