If S = z ∈ C: ( Z -i/ z +2 i) ∈ R then :

Question

If S = z ∈ C: ( Z -i/ z +2 i) ∈ R then : (A) S contains exactly two elements (B) S contains only one element (C) S is a circle in the complex plane (D) S is a straight line in the complex plane

Tardigrade Admin · Accepted Answer

Given ( z - i / z +2 i ) ∈ R Then arg (( z - i / z +2 i )) is 0 or Π <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5eece0f95db8cd519e222d37f0b21566-.png" /> ⇒ S is straight line in complex

Q. If $S = {z \in C : \frac{Z - i}{z + 2 i} \in R}$ , then :

S contains exactly two elements

S contains only one element

S is a circle in the complex plane

S is a straight line in the complex plane

Given $\frac{z - i}{z + 2 i} \in R$
Then $ar g (\frac{z - i}{z + 2 i})$ is $0$ or $Π$

$\Rightarrow S$ is straight line in complex

Q. If S={z∈C:z+2iZ−i​∈R}, then :