(a)[3]
Write $u$ in the Cartesian form $x + iy$, where $x$ and $y$ are expressed in terms of $a$.
(b)[2]
Given that $\arg u = \dfrac{1}{4}\pi$, determine the value of $a$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The complex number $u$ is defined by $u = \dfrac{3 + 2i}{a - 5i}$, with $a$ taken to be real.