Q. In the argand plane, the complex number $\mathcal{z} = 4 - 3i$ is turned in the clockwise sense through $180{^\circ}$ and stretched three times. The complex number represented by the new number is
A) $12 + 9i$
B) $12 - 9i$
C) $- 12 - 9i$
D) $- 12 + 9i$
Explanation
(d)
We have, $\mathcal{z} = 4 - 3i$
$\therefore\ \ \left| \mathcal{z} \right| = \sqrt{4^{2} + ( - 3)^{2}} = 5$
Let $\mathcal{z}_{1}$ be the new complex number obtained by rotating $\mathcal{z}$ in the clockwise sense through $180{^\circ}$, therefore
$\mathcal{z}_{1} = - 4 + 3i$
Therefore required complex number is
$3( - 4 + 3i) = - 12 + 9i$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.