Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Set of non zero positive irrational number under complex multiplication for

Set of non zero positive irrational number under complex multiplication form group?

1 Answer

Comment
A)

There are four properties required for a set with an operation to be a group. If SS is the set and ∗∗ is the operation, then these are the properties:

  • For all a,bin S, a∗bis also in S. (closure)
  • For all a,b,c in S, (a∗b)∗c=a∗(b∗c). (associativity)
  • 1 is in S, where, for all a in S, 1∗a=a∗1= a. (identity)
  • For all a in S, some a−1 is in S, such that a∗a^−1=a^−1∗a=1. (inverse)

The set of irrational numbers is not closed under addition or multiplication: for instance, 

- √2+2=0

(-√2)( √2)=-2

 

The real numbers are a group, if addition is used as the operation. (Only the nonzero real numbers with multiplication are a group.)

This proves that the irrational numbers are not closed but that the real numbers are a group,half the elements of a commutative group (like the real numbers with addition) will not be a closed subset, unless it it is the whole group.

Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...