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

Problem

(−10+√(,−40))/2

Solution

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

√(,−40)=√(,−1⋅40)

√(,−40)=i√(,40)

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

√(,40)=√(,4⋅10)

√(,40)=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+i√(,10)

Final Answer

(−10+√(,−40))/2=−5+i√(,10)

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