Q: 3√z + 5 = 4, so we have √z = -1/3 ··· Eq.1
Since √z is negative, z must be the square or the product of negative real numbers.
So that we use the rules of imaginary numbers, The i-Part First, such as i = √-1 or i² = -1.
From Eq.1, √z = (-1) x (1/3) = i² x 1/3, so √z = i²/3 To undo the root, square both sides.
We have: z = (i²/3)² = (i²/3) x (i²/3) = (-1/3) x (-1/3), or z = (i²/3)² = i² x i²/9 = (-1) x (-1/9)
CK: √z = √(-1/3 x -1/3) = √(-1/3) x √(-1/3) = -1/3, or
√z = √(-1 x -1/9) = √-1 x √(-1/9) = (i) x (i/3) = i²/3 = -1/3, so that
3√z + 5 = 3 x (-1/3) + 5 = -1 + 5 = 4 CKD.
Therefore, the answere is z = (-1/3) x (-1/3), or z = (-1) x (-1/9).