(i(a))[3]
You are told that $u$ is a root of the equation $2x^3 - x^2 + 4x + k = 0$, where $k$ is a constant. Show all working and do not use a calculator. Find the value of $k$.
(i(b))[4]
Show all working and do not use a calculator to find the other two roots of this equation.
(ii)[4]
On an Argand diagram, sketch the locus of points representing complex numbers $z$ that satisfy $|z - u| = 1$. Find the least value of $\arg z$ for points on this locus. Give your answer in radians, correct to 2 decimal places.