Answered: Prove that The set of all complex…

Prove that The set of all complex number is a group under multiplication, and G={1,-1,i,-i} is a non-trivial subgroup of C.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 36E

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Question

1-Prove that The set of all complex number is a group under multiplication, and G={1,-1,i,-i} is a non-trivial subgroup of C.

2- H={[1],[2],[4]} forms a subgroup of 〖Z_7^*=Z〗_7-[0] under multiplication. Are H of the group G is a subgroup of G?

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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