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For a non-zero complex number z, let arg(z) denote the principal argument with - π < arg(z) ≤ π. Then, which of the following statement(s) is (are) FALSE?
  • a)
  • b)
    The function  defined by f(t) = arg ( −1 + it ) for all t ∈ R , is continuous at all points of R, where 
  • c)
    For any two non-zero complex numbers z1 and z is an integer multiple of 2π
  • d)
    For any three given distinct complex numbers z1,z2 and zthe locus of the point z satisfying the condition  , lies on a straight line
Correct answer is option 'A,B,D'. Can you explain this answer?
Verified Answer
For a non-zero complex number z, let arg(z) denote the principal argum...
(A) The argument of the complex number is calculated as follows.

Hence, option (A) is false.
(B) The definition of the function f(t) = arg ( −1 + it ) is,

It is clear from the definition of the function that the function is discontinuous at t =0 .
Hence, option (B) is false.
(C) The value of 
is calculated as follows..

Hence, option (C) is true.
(D) If,

Then,

is a real number
Hence  are concyclic. That is,

Hence, option (D) is false.
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For a non-zero complex number z, let arg(z) denote the principal argument with - π < arg(z) ≤ π. Then, which of the following statement(s) is (are) FALSE?a)b)The functiondefined byf(t) = arg ( −1 + it ) for all t ∈ R , is continuous at all points of R,wherec)For any two non-zero complex numbers z1and z2is an integer multiple of 2πd)For any three given distinct complex numbers z1,z2and z3the locus of the point z satisfying the condition,lies on a straight lineCorrect answer is option 'A,B,D'. Can you explain this answer?
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For a non-zero complex number z, let arg(z) denote the principal argument with - π < arg(z) ≤ π. Then, which of the following statement(s) is (are) FALSE?a)b)The functiondefined byf(t) = arg ( −1 + it ) for all t ∈ R , is continuous at all points of R,wherec)For any two non-zero complex numbers z1and z2is an integer multiple of 2πd)For any three given distinct complex numbers z1,z2and z3the locus of the point z satisfying the condition,lies on a straight lineCorrect answer is option 'A,B,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about For a non-zero complex number z, let arg(z) denote the principal argument with - π < arg(z) ≤ π. Then, which of the following statement(s) is (are) FALSE?a)b)The functiondefined byf(t) = arg ( −1 + it ) for all t ∈ R , is continuous at all points of R,wherec)For any two non-zero complex numbers z1and z2is an integer multiple of 2πd)For any three given distinct complex numbers z1,z2and z3the locus of the point z satisfying the condition,lies on a straight lineCorrect answer is option 'A,B,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a non-zero complex number z, let arg(z) denote the principal argument with - π < arg(z) ≤ π. Then, which of the following statement(s) is (are) FALSE?a)b)The functiondefined byf(t) = arg ( −1 + it ) for all t ∈ R , is continuous at all points of R,wherec)For any two non-zero complex numbers z1and z2is an integer multiple of 2πd)For any three given distinct complex numbers z1,z2and z3the locus of the point z satisfying the condition,lies on a straight lineCorrect answer is option 'A,B,D'. Can you explain this answer?.
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