(i) To find \(a\) and \(b\), substitute \(x = 2 - i\) into the equation \(x^3 + ax^2 - 3x + b = 0\). Calculate \((2-i)^3\) and \((2-i)^2\), and equate real and imaginary parts to zero.

\((2-i)^2 = 4 - 4i + i^2 = 3 - 4i\)

\((2-i)^3 = (2-i)(3-4i) = 6 - 8i - 3i + 4i^2 = 2 - 11i\)

Substitute into the equation: \((2 - 11i) + a(3 - 4i) - 3(2 - i) + b = 0\)

Equate real parts: \(2 + 3a - 6 + b = 0\)

Equate imaginary parts: \(-11 - 4a + 3 = 0\)

Solve these equations to find \(a = -2\) and \(b = 10\).

(ii) On the Argand diagram, draw a circle with center \(2 - i\) and radius 1. Also, draw the perpendicular bisector of the line segment joining \(0\) to \(-i\). Shade the region inside the circle and on the side of the bisector closer to \(0\).