(a) Multiply numerator and denominator by \(1 + i\):

\(u = \frac{(7+i)(1+i)}{(1-i)(1+i)}\)

\(= \frac{7 + 7i + i + i^2}{1 + i - i - i^2}\)

\(= \frac{7 + 8i - 1}{2}\)

\(= \frac{6 + 8i}{2}\)

\(= 3 + 4i\)

(b) Plot the points on an Argand diagram:

Point A at \((3, 4)\), point B at \((7, 1)\), and point C at \((1, -1)\).

(c) Calculate arguments:

\(\arg(1-i) = -\frac{1}{4}\pi\)

\(\arg(7+i) = \arctan\left(\frac{1}{7}\right)\)

\(\arg(u) = \arg(7+i) - \arg(1-i)\)

\(\arctan\left(\frac{4}{3}\right) = \arctan\left(\frac{1}{7}\right) + \frac{1}{4}\pi\)