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

Problem

(−12+√(,−18))/60

Solution

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

√(,−18)=√(,18)⋅i

2. Factor the radicand to simplify the square root further, noting that 18=9⋅2

√(,9⋅2)⋅i=3√(,2)*i

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

(−12+3√(,2)*i)/60

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

(3*(−4+√(,2)*i))/60

5. Divide the numerator and denominator by their common factor of 3

(−4+√(,2)*i)/20

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

(−4)/20+(√(,2)*i)/20

7. Reduce the real part by dividing both the numerator and denominator by 4

−1/5+√(,2)/20*i

Final Answer

(−12+√(,−18))/60=−1/5+√(,2)/20*i

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