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Consider the functionof a complex variableThe singularities of f(z) are as follows:
  • a)
    Branch points at z=1 and z=∞; and a pole at z=0 for all θ
  • b)
    Branch points at z=0,z=1 and z = ∞
  • c)
     
    Branch points at z=1 and z=∞ and a pole at z=0 for all θ other than 0 < θ < 2π
  • d)
    Branch points at z=1 and z=∞; and a pole at z=0 only for 0≤ θ < 2π
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the functionof a complex variableThe singularities of f(z)are...
The given function is,

Now, put w=0 in equation (ii) is

z=∞ is a branch point
Put z=1 in equation (i)
f(1)=1ln⁡(1−1)=ln⁡0 (undefined)
z=1 is also a branch point
Put z=0 in equation (i) ,


z=0 is also a branch point
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Consider the functionof a complex variableThe singularities of f(z)are as follows:a)Branch points atz=1andz=∞; and a pole atz=0for allθb)Branch points atz=0,z=1and z =∞c)Branch points atz=1andz=∞and a pole atz=0for allθother than 0 <θ < 2πd)Branch points atz=1andz=∞; and a pole atz=0only for0≤θ < 2πCorrect answer is option 'C'. Can you explain this answer?
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Consider the functionof a complex variableThe singularities of f(z)are as follows:a)Branch points atz=1andz=∞; and a pole atz=0for allθb)Branch points atz=0,z=1and z =∞c)Branch points atz=1andz=∞and a pole atz=0for allθother than 0 <θ < 2πd)Branch points atz=1andz=∞; and a pole atz=0only for0≤θ < 2πCorrect answer is option 'C'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about Consider the functionof a complex variableThe singularities of f(z)are as follows:a)Branch points atz=1andz=∞; and a pole atz=0for allθb)Branch points atz=0,z=1and z =∞c)Branch points atz=1andz=∞and a pole atz=0for allθother than 0 <θ < 2πd)Branch points atz=1andz=∞; and a pole atz=0only for0≤θ < 2πCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the functionof a complex variableThe singularities of f(z)are as follows:a)Branch points atz=1andz=∞; and a pole atz=0for allθb)Branch points atz=0,z=1and z =∞c)Branch points atz=1andz=∞and a pole atz=0for allθother than 0 <θ < 2πd)Branch points atz=1andz=∞; and a pole atz=0only for0≤θ < 2πCorrect answer is option 'C'. Can you explain this answer?.
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