The point $A$ represents a fixed complex number $a$ where \(\frac{\pi}{4}

Question

The point $A$ represents a fixed complex number $a$ where $\frac{\pi}{4} < \arg(a) < \frac{\pi}{2}$. The complex numbers $-ia$ and $-a$ are represented by the points $B$ and $C$ respectively. On a single clearly labelled Argand diagram, mark the points $A$, $B$ and $C$. Describe the geometrical relationship between $A$ and $B$, and $A$ and $C$.

Accepted Answer

(i) $B$ is obtained by rotating $A$ clockwise through $\dfrac\pi2$ about $O$, with $OB=OA$ (ii) $C$ is obtained by rotating $A$ through $\pi$ about $O$, with $OC=OA$

2023 TJC NYJC VJC FM P1 Q6

2023 TJC NYJC VJC FM P1 Q6

Video Solution:

Solution:

Solution locked