0 votes 0 votes In the above question my doubt is instead of under multiplication if we change under ADDITION then what is its value?plz someone explain details. Set Theory & Algebra discrete-mathematics general-topic-doubt set-theory&algebra group-theory + – dileswar sahu asked Oct 11, 2016 edited Mar 9, 2019 by Abdul Wazeed dileswar sahu 306 views answer comment Share Follow See 1 comment See all 1 1 comment reply Habibkhan commented Oct 11, 2016 reply Follow Share First of all to have order we need to define the identity element w.r.t addition which should be 0.Also we can write the complex number as : cos π/4 + i sin π/4 . So order as we know is the smallest index n for an element a such that an = e where e is the identity element of that operation and n is positve. So we have to find the smallest power n for the above complex no s.t. (cos π/4 + i sin π/4)n = e = 0(since 0 is additive identity) ⇒ (cos π/4 + i sin π/4) + (cos π/4 + i sin π/4) + ...+ (cos π/4 + i sin π/4) = 0 [ total of n terms and since addition is concerned operation) But the value cos π/4 + i sin π/4 in fact > 0 , hence it is not possible to get sum = 0 since the complex number is > 0 and n also > 0 Hence order does not exist if you consider addition operation here. 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes under ADDITION, it doesn't satisfied group property. so we can't find out order. Rajnish Kumar answered Oct 11, 2016 Rajnish Kumar comment Share Follow See all 0 reply Please log in or register to add a comment.