Last year, I shared a handful of random interesting questions from the 2016 Prelims. Students feedback that they were quite helpful and gave them good exposure. I thought I share some that I’ve seen this year. I know, its a bit early for Prelims. But ACJC just had their paper 1. 🙂

This is from ACJC 2017 Prelims Paper 1 Question 7. And it is on complex numbers.

7
(a) Given that $2z + 1 = |w|$ and $2w-z = 4+8i$, solve for $w$ and $z$.

(b) Find the exact values of $x$ and $y$, where $x, y \in \mathbb{R}$ such that $2e^{-(\frac{3+x+iy}{i})} = 1 -i$

I’ll put the solutions up if I’m free.

But for students stuck, consider checking this link here for (a) and this link here for (b). These links hopefully enlightens students.

Just FYI, you cannot $\text{ln}$ complex numbers as they are not real…