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Joint Entrance Examination
Mathematics
Complex Numbers
Question 229
Question 229 of 455
Medium
MCQ
If
S
=
{
z
∈
C
:
z
−
i
z
+
2
i
∈
R
}
S=\left\{z\in\mathbb C:\dfrac{z-i}{z+2i}\in\mathbb R\right\}
S
=
{
z
∈
C
:
z
+
2
i
z
−
i
∈
R
}
, then
A
S
S
S
contains exactly two elements.
B
S
S
S
contains only one element.
C
S
S
S
is a circle in the complex plane.
D
S
S
S
is a straight line in the complex plane.
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Official solution
Given \[{{z - i} \over {z + 2i}} \in R\] Then \[\arg \left( {{{z - i} \over {z + 2i}}} \right)\] is 0 or \[\pi \] \[\Rightarrow\] S is straight line in complex
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