Let \( \mathrm{s}, \mathrm{t}, \mathrm{r} \) be non-zero complex nu...

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Let \( \mathrm{s}, \mathrm{t}, \mathrm{r} \) be non-zero complex numbers and \( \mathrm{L} \) be the set of solutions \( \mathrm{z}=\mathrm{x}+\mathrm{iy}(\mathrm{x}, \mathrm{y} \in \mathbf{R}, \mathrm{i}=\sqrt{-1}) \) of the equation \( s z+t \bar{z}+r=0 \), where \( \bar{z}=x- \) iy. Then which of the following statement(s) is(are)
\( \mathrm{P} \) TRUE?
(A) If \( \mathrm{L} \) has exactly one element, then \( |\mathrm{s}| \neq|\mathrm{t}| \)
W
(B) If \( |\mathrm{s}|=|\mathrm{t}| \), then \( \mathrm{L} \) has infinitely many elements
(C) The number of elements in \( \mathrm{L} \cap\{\mathrm{z}:|\mathrm{z}-1+\mathrm{i}|=5\} \) is at most 2
(D) If \( \mathrm{L} \) has more than one element, then \( \mathrm{L} \) has infinitely many elements.
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