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MATH2521 COMPLEX ANALYSIS

CLASS TEST 1

Question 1

Copy the following statement in your own handwriting:

“I declare that all the work I have submitted for class test 1 in MATH2521 Complex Analysis, term 3, 2020 is my own work.”

Then sign the statement, scan it together with your student ID card, and upload the file.

Question 2    (2 marks)

Prove that if then

Question 3    (6 marks)

Let be the line in the complex plane.

(a) Find the image of under the complex transformation  Sketch your answer.

(b) With no further calculations, sketch the image of under the transformation

Question 4    (6 marks)

Show that the complex function

is differentiable at one point only, and find this point.

Question 5    (3 marks)

Where is the function defined by

holomorphic? Give detailed reasons. Note. Inefficient solutions with lots of calculation will not earn good marks!

Question 6    (3 marks)

Let Show that

for some integer , and find the value of .