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JEE Main 202229 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2022 · 29 June · Evening Shift · Mathematics · Complex Number

Let (z) represent the principal argument of the complex number z ....

Let (z)\left(z\right) represent the principal argument of the complex number zz. The, \left|z\right| = 3 and arg(z−1)−arg(z+1)=π4arg\left(z - 1\right) - arg\left(z + 1\right) = \dfrac{\pi}{4} intersect:Let (z) represent the principal argument of the complex number z . The, |z| = 3 and arg(z - 1) - arg(z + 1) = (π)/(4)

Options

  1. AExactly at one point
  2. BExactly at two points
  3. CNowhere
  4. DAt infinitely many points.

Correct answer

C. Nowhere

Step-by-step solution

Let (z)\left(z\right) represent the principal argument of the complex number zz.

The, \left|z\right| = 3willrepresentacirclewithcentre(0,0)andradiuswill represent a circle with centre \left(0, 0\right) and radius3\text{units}</p><p>And</p><p>Andarg\left(z - 1\right) - arg\left(z + 1\right) = \dfrac{\pi}{4}willrepresentarcofthecirclewithcentre(0,1)will represent arc of the circle with centre \left(0, 1\right) and radius 2\sqrt{2}, now on plotting the diagram,

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

We can see they are intersecting nowhere.

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