Simplify (-12+ square root of -18)/60

Problem

(−12+√(,−18))/60

Solution

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

√(,−18)=√(,18)⋅i

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

√(,18)=√(,9⋅2)=3√(,2)

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

(−12+3*i√(,2))/60

4. Factor out the greatest common factor from the terms in the numerator.

3*(−4+i√(,2))

5. Divide the numerator and the denominator by their greatest common divisor, which is 3

(3*(−4+i√(,2)))/60=(−4+i√(,2))/20

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

(−4)/20+(i√(,2))/20

7. Reduce the first fraction to its simplest form.

−1/5+√(,2)/20*i

Final Answer

(−12+√(,−18))/60=−1/5+√(,2)/20*i

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