Complex Analysis Answers

Find the laurent series for (1-exp2z)/z

Use the Binomial theorem, write the number (1 + 2i)^12 in the form a + ib.

Show that u(x,y)=e^xcosy and v(x,y)=e^xsiny are harmonic for all values of (x,y).

Show that the function f(z) = x^2 + y^2 + i 2xy has a derivative only at points that lie on

the x-axis.

   On the first day of the month, 4 customers come to a restaurant. Afterwards, those 4 customers come to the same restaurant once in 2,4,6 and 8 days respectively.

a)     On which day of the month, will all the four customers come back to the restaurant together?

b)     Briefly explain the technique you used to solve (a).

Which of the following sets are closed in C. (Justify your answer)

a) A={z∈C:Rez<1}∪{z∈C:Imz≥1}

b) B={z∈C:-∞<x≤3}