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Complex Numbers question

2018 · Shift 2 · Q23

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2018 · Shift 2 · Q23

Complex Numbers question

2018 · Shift 2 · Q23

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −1

Let s, t, r be non-zero complex numbers and L be the set of solutions

z = x + iy(x,y \in R,\,i = \sqrt { - 1} )

of the equation

sz + t\overline z + r = 0

where

\overline z

= x

-

iy. Then, which of the following statement(s) is(are) TRUE?

A
If L has exactly one element, then |s| $e$ |t|
B
If |s| = |t|, then L has infinitely many elements
C
The number of elements in $L \cap \{ z:|z - 1 + i| = 5\}$ is at most 2
D
If L has more than one element, then L has infinitely many elements

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