Let $\mu$ stand for the complex number $-1 + \sqrt{7}i$. It is stated that $\mu$ is a root of $2x^3 + 3x^2 + 14x + k = 0$, where $k$ is a real constant.
(a)[3]
Find the value of $k$.
(b)[4]
Find the remaining two roots of the equation.
(c)[2]
On an Argand diagram, sketch the locus of points for complex numbers $z$ that satisfy $|z - u| = 2$.
(d)[2]
Determine the largest value of $\arg z$ for points on this locus, and express your answer in radians.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=-1+\sqrt7 i$ and try to expand it” …