Evaluate

Problem

(√(,−36)√(,−49))/√(,−16)

Solution

1. Express each square root in terms of the imaginary unit i where √(,−1)=i

2. Simplify the numerator by calculating the square roots of the negative numbers.

√(,−36)=6*i

√(,−49)=7*i

3. Simplify the denominator by calculating the square root of the negative number.

√(,−16)=4*i

4. Substitute these values back into the original expression.

((6*i)*(7*i))/(4*i)

5. Multiply the terms in the numerator.

6*i⋅7*i=42*i2

6. Apply the identity i2=−1 to the numerator.

42*(−1)=−42

7. Divide the numerator by the denominator.

(−42)/(4*i)

8. Rationalize the denominator by multiplying the top and bottom by i

(−42*i)/(4*i2)

9. Simplify the expression using i2=−1 again.

(−42*i)/(−4)

10. Reduce the fraction to its simplest form.

(21*i)/2

Final Answer

(√(,−36)√(,−49))/√(,−16)=21/2*i

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