JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q2

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MathematicsSingle correct+4 / -1Question 2 of 90

Let $\arg(z)$ represent the principal argument of the complex number $z$ . Then, $|z|=3$ and $\arg(z-1)-\arg(z+1)=\dfrac\pi4$ intersect

exactly at one point.

exactly at two points.

nowhere.

at infinitely many points.

Answer and worked solution

Official answer: C

Locus. The segment from $-1$ to $1$ subtends $\frac\pi4$ at $z$ : an arc of a circle through $\pm1$ with radius $\sqrt2$ and centre $(0,\pm1)$ . Its farthest point from the origin is at distance $1+\sqrt2<3$ .

So it never meets $|z|=3$ .

(C)

Topics:Geometry in the complex plane Modulus and argument

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 2