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

Problem

(−20+√(,−50))/60

Solution

1. Simplify the radical by expressing the square root of a negative number in terms of the imaginary unit i

√(,−50)=√(,−1⋅25⋅2)

√(,−50)=5*i√(,2)

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

(−20+5*i√(,2))/60

3. Factor out the greatest common factor from the numerator to prepare for division.

5*(−4+i√(,2))

4. Divide the numerator and the denominator by their greatest common divisor, which is 5

(5*(−4+i√(,2)))/60=(−4+i√(,2))/12

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

(−4)/12+(i√(,2))/12

−1/3+√(,2)/12*i

Final Answer

(−20+√(,−50))/60=−1/3+√(,2)/12*i

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