Question

Complex Numbers & Roots
1/2x^2=-28

Answer 1

Take the reciprocal on both sides to get \[2x^2 = -1/28\] divide both side by 2 to get \[x^2 = -1/56\] by definition, \[\sqrt{-1} = i\] so take the square root of both sides of the equation to get \[x = \sqrt{(-1/56)}\] and also, by definition we know that \[\sqrt{a/b} = \sqrt{a}/\sqrt{b}\] and using this definition, we apply it to get \[x = \sqrt{-1}/\sqrt{56}\] and using the definition of square root of -1, we get \[x = i/\sqrt{56}\] you simplify the square root of 56 further. I'll leave it up to you...