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Algebra Level 4

Which of the following is the locus of the equation: $\text{arg} \left [\frac{z-1}{z} \right] = \frac{\pi}{2}$ , where $z=x+iy$ ?

A C B D

1 solution

Arpon Paul
Dec 3, 2015

We know, $arg(\frac{z_1}{z_2}) = arg(z_1) - arg(z_2)$ .

We also know that an angle in a semicircle is a right angle.

Now, have a look at the figures:

Fig 1

Fig 2

From this figures, it is clear that C is the right answer.