Let $s , t , r$ be non-zero complex numbers and $L$ be the set of solutions $z = x + i y ( x , y \in \mathbb { R } , i = \sqrt { - 1 } )$ of the equation $s z + t \bar { z } + r = 0$, where $\bar { z } = x - i y$. Then, which of the following statement(s) is (are) TRUE? (A) If $L$ has exactly one element, then $| s | \neq | t |$ (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
Let $s , t , r$ be non-zero complex numbers and $L$ be the set of solutions $z = x + i y ( x , y \in \mathbb { R } , i = \sqrt { - 1 } )$ of the equation $s z + t \bar { z } + r = 0$, where $\bar { z } = x - i y$. Then, which of the following statement(s) is (are) TRUE?\\
(A) If $L$ has exactly one element, then $| s | \neq | t |$\\
(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