Let z = x + iy be a point in the Argand plane | vedclass

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(D) The condition $\operatorname{Arg}\left(\frac{z - z_1}{z - z_2}\right) = \frac{\pi}{2}$ represents a semicircular arc connecting $z_1$ and $z_2$. \

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a semicircular arc containing the origin

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(D) The condition $\operatorname{Arg}\left(\frac{z - z_1}{z - z_2}ight) = \frac{\pi}{2}$ represents a semicircular arc connecting $z_1$ and $z_2$. \ Here,$z_1 = 3$ and $z_2 = -2i$. \ The locus is a semicircle passing through $(3, 0)$ and $(0, -2)$. \ To check if the origin $(0, 0)$ lies on this arc,we substitute $z = 0$ into the expression: \ $\operatorname{Arg}\left(\frac{0 - 3}{0 + 2i}ight) = \operatorname{Arg}\left(\frac{-3}{2i}ight) = \operatorname{Arg}\left(\frac{3i}{2}ight) = \frac{\pi}{2}$. \ Since the condition is satisfied at $z = 0$,the locus is a semicircular arc containing the origin.

Let $z = x + iy$ be a point in the Argand plane. If the amplitude of $\left(\frac{z - 3}{z + 2i}\right)$ is $\frac{\pi}{2}$,then the locus of $z$ is

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