Simplify (-20+ square root of -75)/40

Problem

(−20+√(,−75))/40

Solution

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

√(,−75)=√(,−1⋅75)

√(,−75)=i√(,75)

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

√(,75)=√(,25⋅3)

√(,75)=5√(,3)

√(,−75)=5*i√(,3)

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

(−20+5*i√(,3))/40

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

5*(−4+i√(,3))

5. Divide both the numerator and the denominator by their greatest common factor, which is 5

(5*(−4+i√(,3)))/40=(−4+i√(,3))/8

6. Rewrite the expression in standard form a+b*i

(−4)/8+(i√(,3))/8

−1/2+√(,3)/8*i

Final Answer

(−20+√(,−75))/40=−1/2+√(,3)/8*i

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