Task 3A mapping f :C → C is called bounded, ifsup |f(2)| < 0.zECShow that sin, cos : C → C are unbounded (i.e. not bounded).Task 4Let M =E R2x2 and let Mc : C+C be defined viaMc(x + iy) := ar + by + i(cx + dy).The following statements are equivalent:(i) Mc(i) = iMc(1);(ii) M E C;(iii) 3a eC Vz EC: Mc(2) = az;( iv) V2, A , w C: Mc(z + λω) - Μc(2) + λMc().

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A mapping f:C→ C is called bounded, if sup |f(2)| < o0. zEC Show that sin, cos : C →C are unbounded (i.e. not bounded).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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Question

Task 3
A mapping f :C → C is called bounded, if
sup |f(2)| < 0.
zEC
Show that sin, cos : C → C are unbounded (i.e. not bounded).
Task 4
Let M =
E R2x2 and let Mc : C+C be defined via
Mc(x + iy) := ar + by + i(cx + dy).
The following statements are equivalent:
(i) Mc(i) = iMc(1);
(ii) M E C;
(iii) 3a eC Vz EC: Mc(2) = az;
( iv) V2, A , w C: Mc(z + λω) - Μc(2) + λMc().

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