Show that there is only one linear fractional transformation that maps three given distinct points z1, z2 and z3 in the extended z plane onto three specified distinct points w1, w2 and w3 in the extended w plane.
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Find the image of the semi-infinite strip x > 0, 0 < y < 1 when . Sketch the strip and its image.
Prove that the linear fractional transformation maps the circle
into itself. Also prove
that f(z) is conformal in .
Factor x5 - 1 over . Give the generator polynomials of all cyclic codes of length five over
.
he aim of this exercise is to show that every binary repetition code of odd length is perfect.
i) Find the value of t and d for a binary repetition code of length . \hfill (2)
ii) Show that
(Hint: Start with the relation
iii) Deduce that every repetition code of odd length is perfect.
Find the zeros and singularities of the function in
. Also find the residue at the poles
Show that there is only one linear fractional transformation that maps three given distinct points z1, z2 and z3 in the extended z plane onto three specified distinct points w1, w2 and w3 in the extended w plane.
Evaluate where c is the circle
.