Question

Let arg(z) represent the principal argument of the complex number z. Then, |z | = 3 and arg(z - 1) - arg(z + 1) = π/4 intersect

• A. exactly at one point
• B. exactly at two points
• C. nowhere
• D. at infinitely many points

Answer 1

Answer: (A)

exactly at one point

Answer 2

The correct answer is (C) : nowhere

Fig.

|z| = 3
arg(z-1) - arg(z+1) = π/4
$∠AKL = ∠ACB = \frac{π}{4}$
⇒ LK = AL = α = 1
K(0,1)
Radius = $\sqrt2$
PL = PK + KL = $\sqrt2 + 1$
P(0,1 + $\sqrt2$)
Therefore , Number of intersection = 0