Evaluate (-10+ square root of -40)/2

Problem

(−10+√(,−40))/2

Solution

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

√(,−40)=√(,40)⋅i

2. Simplify the radical by factoring out the largest perfect square from 40.

√(,40)=√(,4⋅10)=2√(,10)

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

(−10+2*i√(,10))/2

4. Divide each term in the numerator by the denominator to simplify the fraction.

(−10)/2+(2*i√(,10))/2

5. Simplify the resulting terms.

−5+i√(,10)

Final Answer

(−10+√(,−40))/2=−5+i√(,10)

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