Simplify (-2+ square root of -8)/2

Problem

(−2+√(,−8))/2

Solution

1. Express the square root of a negative number using the imaginary unit i

√(,−8)=√(,−1⋅8)

√(,−8)=i√(,8)

2. Simplify the radical by factoring out the largest perfect square.

√(,8)=√(,4⋅2)

√(,8)=2√(,2)

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

(−2+2*i√(,2))/2

4. Factor out the common factor of 2 from the numerator.

(2*(−1+i√(,2)))/2

5. Divide the numerator and denominator by 2 to reach the final simplified form.

−1+i√(,2)

Final Answer

(−2+√(,−8))/2=−1+i√(,2)

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