Consider the function below. a) state the singularity of f(z). b) what is the kind of singularity of f(z).

      

Consider the function

a) state the singularity of f(z).
b) what is the kind of singularity of f(z).
c) find the Laurent series of f(z).
d) what is the region of convergence of f(z)?.

  

Answers

---

d) The series converges for all values of z i.e. the series converges on the whole
of z plane.

---

sharon kalunda answered the question on May 10, 2019 at 13:52

Next: Define firewall.
Previous: Consider the function

View More Complex Analysis 1 Questions and Answers | Return to Questions Index

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

---

• Consider the function a) state the singularity of f(z). b) what is the kind of the singularity of f(z).(Solved)
  

  Consider the function
  
  a) state the singularity of f(z).
  b) what is the kind of the singularity of f(z).
  c) expand f(z) in a Laurent series.
  d) state the region of convergence of the series.

  Date posted: May 10, 2019.  Answers (1)

• Show that the function below has an essential singularity at z = 3.(Solved)
  

  Show that the function below has an essential singularity at z = 3.
  

  Date posted: May 10, 2019.  Answers (1)

• Define a Pole(Solved)
  

  Define a Pole

  Date posted: May 10, 2019.  Answers (1)

• Define Isolated Singular points.(Solved)
  

  Define Isolated Singular points.

  Date posted: May 10, 2019.  Answers (1)

• Define the Taylor’s Series from Laurent Series(Solved)
  

  Define the Taylor’s Series from Laurent Series

  Date posted: May 10, 2019.  Answers (1)

• a) Integrate z² along the straight line OM (direct) and also along the path OLM consisting of two straight line segments OL and LM. O is...(Solved)
  

  a) Integrate z² along the straight line OM (direct) and also along the path OLM
  consisting of two straight line segments OL and LM. O is the origin and M is the
  point z = 3 + i.
  b) Show that the integral of z² along the two different paths are equal.
  c) Is the result true for any function other than z² for the two paths?

  Date posted: May 10, 2019.  Answers (1)

• Evaluate the following expression(Solved)
  

  
  

  Date posted: May 10, 2019.  Answers (1)

• a)Evaluate the following expression where c is any simple closed curve c and a is inside c,(Solved)
  

  a)Evaluate the following expression where c is any simple closed curve c and a is inside c,
  
  b) What is the value of the integral if a is outside the closed curve?

  Date posted: May 10, 2019.  Answers (1)

• If f(z) is analytic inside and on the boundary c of a simply connected region R and a is any point inside the curve c then,(Solved)
  

  If f(z) is analytic inside and on the boundary c of a simply connected region R and a is
  any point inside the curve c then,
  
  Prove

  Date posted: May 10, 2019.  Answers (1)

• Find the fixed points of the bilinear transformation(Solved)
  

  Find the fixed points of the bilinear transformation
  

  Date posted: May 10, 2019.  Answers (1)

• Find the fixed points of the bilinear transformation(Solved)
  

  Find the fixed points of the bilinear transformation
  

  Date posted: May 10, 2019.  Answers (1)

• a) Find a bilinear transformation, which transforms the unit circle |z| = 1 into the real axis of the w plane in such a way that...(Solved)
  

  a) Find a bilinear transformation, which transforms the unit circle |z| = 1 into the real
  axis of the w plane in such a way that the points z_{1 = 1, z2 = i, z3 = -1 are mapped onto w1 = 0, w2 = 1, w3 = infinite.
  b) In what regions the interior and exterior of the circle are mapped.}

  Date posted: May 10, 2019.  Answers (1)

• Find a bilinear transformation which maps the points(Solved)
  

  

  Date posted: May 10, 2019.  Answers (1)

• Find a bilinear transformation which maps the point z = 0, -i, -1 on the z plane into w = i, 1, 0 respectively on the...(Solved)
  

  Find a bilinear transformation which maps the point z = 0, -i, -1 on the z plane into
  w = i, 1, 0 respectively on the w plane.

  Date posted: May 10, 2019.  Answers (1)

• Explain the nature of the transformation w = z² considering the semi-circle with centre the origin and the radius r on the z –plane(Solved)
  

  Explain the nature of the transformation w = z² considering the semi-circle with centre
  the origin and the radius r on the z –plane.

  Date posted: May 10, 2019.  Answers (1)

• Let w = 3z + 4 – 5i = f(z) Find the values of w which corresponds to z = -3 + i on the z...(Solved)
  

  Let w = 3z + 4 – 5i = f(z)
  Find the values of w which corresponds to z = -3 + i on the z plane.

  Date posted: May 10, 2019.  Answers (1)

• Find the image of the point (4, 3) on z plane under the transformation w = 2z² + 3.(Solved)
  

  Find the image of the point (4, 3) on z plane under the transformation w = 2z² + 3.

  Date posted: May 10, 2019.  Answers (1)

• Prove that sin z = sin x cos hy + i cos x sin hy(Solved)
  

  Prove that sin z = sin x cos hy + i cos x sin hy

  Date posted: May 10, 2019.  Answers (1)

• Find all values of z such that(Solved)
  

  Find all values of z such that
  

  Date posted: May 10, 2019.  Answers (1)

• Find all values of z such that e^z = 2(Solved)
  

  Find all values of z such that e^z = 2

  Date posted: May 10, 2019.  Answers (1)