Question:

Let s, t, r be the non-zero complex numbers and L be the set of solutions z = x + iy (x, y ∈ R, i = √-1) of the equation z + t¯z + r = 0, where ¯z = x - iy. Then, which of the following statement(s) is (are) TRUE?

If L has exactly one element, then |s| ≠ |t|

If |s| = |t|, then L has infinitely many elements

If L has more than one element, then L has infinitely many elements

The number of elements in L ∩ {z: |z + i| = 5} is at most 2

C The number of elements inL∩z:|z𕒵+i|=5is at most2