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<e> Evaluate the integral ∮c= 1 /(z-1)(z-2)(z-4) dz where C is |z| = 3 ?




Find the billianear transformation which maps the points z=0,1,∞ on to the points w=0,i,2i.


How do you write the residue at z=∞ where f(z) = 1/z^3+z^5?


A)-2


B)-1


C)1


D)0


Evaluate ∮c e^z/(z+2) (z+3) dz where C is |z|=1?

A)-2

B)-4

C) 1

D) 0

Give one example and also prove that for the complex series which is



1) Conditionally Convergent.



2) Absolutely Convergent.



3) Both.



4) Neither

What is the integral of 1/(z-1) (z-2) (2-4) dz where C is |z| = 3?


Give one example for the complex series which is



1) Conditionally Convergent.



2) Absolutely Convergent.



3) Both.



4) Neither.

Mr McCarthy has a business that manufactures T-shirts. It costs R 30 to produce one shirt and he will sell each shirt for R80. The company can produce a maximum of 70 shirts in a week. a) Write an expression for the total income that will come from producing x number of shirts. b) Write an expression for the weekly expenses for the factory be if x shirts are produced and they have a fixed starting cost of R 1 000. c) Draw the graph showing both the income and expenses on one set of axis. What is the break-even point of the graph? d) e) Mr McCarthy got an order of 300 T-shirts from a company in Canada. What is the cos of a T-shirt in Canadian dollars? The exchange rate is 1 CAD = 8.88 ZAR How much profit per T-shirt will Mr McCarthy make in Canadian dollars? Mr McCarthy quotes the Canadian company 9 $ per T-shirt and then he finds out that the exchange rate has changed to 1 CAD = 10.30 ZAR. Is this a good or a bad thing for Mr McCarthy? Why?


f(z)= z/(z+1)(z+1)^2

The image of straight line 2x-y+3=0 under the transformation w=z-2 is


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