Question

In Argand plane the locus of z ¹ 1 such that arg

$\left\lbrack \frac{2z^{2} - 5z + 3}{3z^{2} - z - 2} \right\rbrack$= $\frac{2\pi}{3}$ is –

• A. The straight line joining the points z = 3/2, z = –2/3
• B. The straight line joining the points z = –3/2, z = 2/3
• C. A segment of a circle passing through z = 3/2, z = –2/3.
• D. A segment of a circle passing through z = –3/2, z = 2/3

Answer 1

Answer: (C)

A segment of a circle passing through z = 3/2, z = –2/3.

Answer 2

Sol. $\frac{2z^{2} - 5z + 3}{3z^{2} - z - 2}$ = $\frac{(2z - 3)(z - 1)}{(3z + 2)(z - 1)}$ = $\frac{2z - 3}{3z + 2}$= $\frac{2}{3}$ . $\frac{z - 3/2}{z + 2/3}$ as z ¹ 1.

\ The given condition reduces to

arg $\left( \frac{z - 3/2}{z + 2/3} \right)$ = $\frac{2\pi}{3}$