Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    14
    Why do analysts care about complex numbers? It's possible to think of lots of different operations between a couple of ordered pairs, and yet for some reason there is a great deal of focus on what happens when we define complex addition/multiplication. Surely there's some explanation other than that they are useful in algebra?
    Offline

    0
    ReputationRep:
    Maybe because the complex addition/multiplication rules are the only ones which give closure of the reals (don't know if that's actually true, just guessing), which is presumably desirable since we want the fundamental theorem of algebra?
    Offline

    17
    ReputationRep:
    I'm pretty certain that *any* field extension of the reals (that preserves commutativity) ends up being isomorphic to the complex numbers. So there aren't actually that many "interesting" possibilities for operations on ordered pairs.

    And of course complex differentiability turns out to be an incredibly powerful concept - far more so than real differentiability.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.