(a) To solve for \(v\) and \(w\), use the equations:

1. \(v + iw = 5\)

2. \((1 + 2i)v - w = 3i\)

Substitute \(w = \frac{5 - v}{i}\) into the second equation:

\((1 + 2i)v - \frac{5 - v}{i} = 3i\)

Simplify and solve for \(v\):

\(v = -\frac{2i}{1+i}\)

Multiply numerator and denominator by the conjugate of the denominator:

\(v = -1 - i\)

Substitute \(v\) back to find \(w\):

\(w = 1 - 6i\)

(b)(i) The equation \(|z - 2 - 3i| = 1\) represents a circle with center \(2 + 3i\) and radius 1.

(b)(ii) The least value of \(\arg z\) is calculated using the geometry of the circle. The answer is \(40.2^\circ\) or \(0.702\) radians.