Evaluate (-8+ square root of -12)/40

Problem

(−8+√(,−12))/40

Solution

1. Simplify the square root of the negative number by using the imaginary unit i where √(,−1)=i

√(,−12)=√(,−1⋅4⋅3)

√(,−12)=2*i√(,3)

2. Substitute the simplified radical back into the original expression.

(−8+2*i√(,3))/40

3. Factor out the greatest common factor from the terms in the numerator.

2*(−4+i√(,3))

4. Divide the numerator and the denominator by their greatest common factor, which is 2

(2*(−4+i√(,3)))/40=(−4+i√(,3))/20

5. Split the fraction into its real and imaginary parts to write it in standard form a+b*i

(−4)/20+(i√(,3))/20

6. Simplify the real part by reducing the fraction.

−1/5+√(,3)/20*i

Final Answer

(−8+√(,−12))/40=−1/5+√(,3)/20*i

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