Let s, t, r be non-zero complex numbers and L be the set of solutions z = x + iy (x, y ∈ R, i = 
) of the equation sz + t 
+ r = 0, where 
= x – iy. Then, which of the following statement(s) is (are) TRUE?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a, c, d)
Sol. sz + t 
+ r = 0, 
= x – iy
(1) + (2)
For unique solution
On solving the above equation we get
| t | ≠ | s |
∴ option is correct
Lines overlap if
| t | = | s | 
∴ 
∴ | t | = | s |
∴ If | t | = | s |, lines will be parallel for sure but it may not be coincident
For option if element of set L represent line, then this line and given circle can have maximum two common points so option is correct
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