Reference no: EM131470300

Please help with the attached question. The following are the comments left by the evaluate r

A1. The fifth roots of unity were properly identified in polar form and a Cayley table of products of these elements was provided as a means of demonstrating closure. In general this is an appropriate method, though an explanation for how the products in the table were determined could not be located. For instance, an explanation for why [cos(6pi/5) + i*sin(6pi/5)] * [cos(8pi/5) + i*sin(8pi/5)] = cos(4pi/5) + i*sin(4pi/5) could not be located.

A2. The Cayley table was referenced as demonstrating the commutative property. An explanation indicating how the table provides this information was not evident.

A3. The element '1' was correctly identified as the identity element of the set. A proof which verifies this claim could not be located, and the reference to the Cayley table was not sufficient.

A4. A statement identifying a general inverse property was made, as was the claim that "from the Cayley table see that every element has multiplicative inverse" which was accompanied by an example. This reference to the Cayley table and the example provided did not sufficiently demonstrate the property, as any details explaining how the table provided this information could not be located. Additionally, a substantiation for how the products in the table were determined is necessary before a proof referencing its entries can be considered for completeness.

A5. Many computations attempting to show the associative property using the elements cos(a) + i*sin(a), cos(b) + i*sin(b), and cos(c) + i*sin(c) were provided. Supporting statements for most lines of the proof could not be located. Additionally, it was not evident that the work specifically addressed the fifth roots of unity, as a, b, and c were defined to be any real numbers and in the work were referred to as integers.