The complex number $u$ is specified as $u = \dfrac{6 - 3i}{1 + 2i}$.
(i)[4]
Working clearly, determine the modulus of $u$ and prove that the argument of $u$ is $-\dfrac{1}{2}\pi$.
(ii)[3]
For complex numbers $z$ satisfying $\arg(z - u) = \dfrac{1}{4}\pi$, determine the smallest possible value of $|z|$.
(iii)[3]
For complex numbers $z$ satisfying $|z - (1 + i)u| = 1$, determine the greatest possible value of $|z|$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Multiply the numerator and denominator by $(1-2i)$, or by an equivalent factor” …