Do not use a calculator in answering this question. The complex number $z$ is such that \(|z|

Question

Do not use a calculator in answering this question. The complex number $z$ is such that $|z|=\sqrt{10}$ and $\arg(z)=-\tan^{-1}3$. Find $z$ in the form $a+bi$, where $a$ and $b$ are integers.[2] In an Argand diagram, $O$ is the origin and the point $A$ represents $z$. The points $B$ and $C$ are such that $OABC$ is a rectangle described in an anti-clockwise sense and $OC=2OA$. Find the complex numbers represented by $B$ and $C$.[4]

Accepted Answer

(a) $z=1-3i$ (b) $B:7-i$, $C:6+2i$

2026 TJC P1 Q4

2026 TJC P1 Q4

Video Solution:

Solution:

Solution locked