Question

In the Argand plane, the vector z=4-3i is turned in the clockwise sense through ${180}^o$ and stretched three times. The complex number represented by the new vector is

• A. 12+9i
• B. 12-9i
• C. -12-9i
• D. -12+9i

Answer 1

The correct option is D

-12+9i

|z|=$\sqrt{4^2+(-{)}^2}$=5

Let $z_1$ be the new vector obtained by rotating

z in the the clockwise sense through ${180}^{\circ }$,

therefore

$z_1$=$e^{-i\pi }z$=(cos$\pi$-isin$\pi$), i.e., z=-4+3i

The unit vector in the direction of $z_1$ is $(-\frac{4}{5}+\frac{3}{5}i)$

Therefore 3|z|$(-\frac{4}{5}+\frac{3}{5}i)$=15$(-\frac{4}{5}+\frac{3}{5}i)$=-12+9i