Simplify (-20+ square root of -50)/60

Problem

(−20+√(,−50))/60

Solution

1. Identify the imaginary component by rewriting the square root of the negative number using the imaginary unit i

√(,−50)=√(,50)⋅i

2. Simplify the radical by factoring out the largest perfect square from 50.

√(,50)=√(,25⋅2)=5√(,2)

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

(−20+5*i√(,2))/60

4. Factor out the greatest common divisor from the terms in the numerator to prepare for simplification.

5*(−4+i√(,2))

5. Divide both the numerator and the denominator by their common factor of 5.

(5*(−4+i√(,2)))/60=(−4+i√(,2))/12

6. Rewrite the expression in standard complex form a+b*i by splitting the fraction.

(−4)/12+(i√(,2))/12

7. Reduce the real part to its simplest fractional form.

−1/3+(i√(,2))/12

Final Answer

(−20+√(,−50))/60=−1/3+(i√(,2))/12

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