Simplify (-12+ square root of -45)/24

Problem

(−12+√(,−45))/24

Solution

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

√(,−45)=√(,−1⋅9⋅5)

√(,−45)=3*i√(,5)

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

(−12+3*i√(,5))/24

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

3*(−4+i√(,5))

4. Divide the numerator and the denominator by their greatest common factor, which is 3

(3*(−4+i√(,5)))/24=(−4+i√(,5))/8

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

(−4)/8+(i√(,5))/8

−1/2+√(,5)/8*i

Final Answer

(−12+√(,−45))/24=−1/2+√(,5)/8*i

Want more problems? Check here!