Complex Analysis Answers

(5+i3) + (2+i8) (convert to polar form)

Let S; T : L^2(0,infinite) -> L^(o,infiniti) be given by
(Sf)(t) = f(2t), (Tf)(t)=f(t/2), f is an element of L^2 (0,infinite).
You are given that S and T are linear mappings L^2(0,infinite) ->L^2(0,infinite), and you need not prove this fact.
i) Calculatr ||S||
ii) Show that T*=2S. Determine S*

[Hint: The usual rules for integration by substitutions also work for the Lebesque integral You need not justify this fact. }

Find the following complex numbers in the form x + iy. a) (1-(sqrt3)i)^85

there are100 people and 100 plates.among 100 people they are divided into three categories rich which take 4plates each,service class 2 plate each and poor .4 poor eat in 1 plate.calculate no of persons of each categories?

find all values of cosh((2k+1)pi(i))/2) k=+-1,+-2......

Find Real of (1-i)^(1+i)

if z1 and z2 are the complex numbers show that
||z1|-|z2||<=|z1+z2|<=|z1|+|z2|

Find the Re(z) of (log(z+4))/(z^2+i)

Find all values of z, e^(2iz)=-1