If z = x + iy, where i = √-1, then what does the equations zz̅ + ∣z∣² + 4(z + z̅) - 48 = 0 represent?

Which one of the following is a square root of $\rm 2a+2\sqrt{a^2 + b^2}$, where a, b ∈ ℝ?

Consider the following statements in respect of the roots of the equation x³ - 8 = 0 :

1. The roots are non-collinear.

2. The roots lie on a circle of unit radius.

Which of the above statements is/are correct?

If i = √-1, then how many values does i^-2n have for different n ∈ ℤ?