What is complex number

  • Thread starter newton1
  • Start date
152
0
actually what is complex number....
i know it's root of the -1
but how can we imagine the kind of number exist??
 
Last edited by a moderator:
Please read this article:
http://physicspost.com/articles.php?articleId=118 [Broken]
 
Last edited:

HallsofIvy

Science Advisor
41,621
821
Of course, you can't DEFINE i as "square root of -1", not because -1 doesn't have a square root, but because, like any number, it has TWO.

Silly "paradoxes" like: i= [sqrt](-1) so i*i= i2= [sqrt](-1)*[sqrt](-1)= [sqrt](-1*-1)= [sqrt](1)= 1 depend on that ambiguity.

When we are working in the real numbers, we can specify sqrt[x] as meaning the POSITVE root. In complex numbers, we don't have any way of distinguishing "positive" or "negative" (the complex numbers cannot be an ordered field).

The way complex numbers are properly defined is as PAIRS of real numbers (a,b) with addition defined as (a,b)+ (c,d)= (a+b, c+d) and multiplication defined as (a,b)*(c,d)= (ac-bd,ad+bc). It then follows that numbers of the form (a,0) act like real numbers while (0,1)*(0,1)= (0*0-1*1,0*1+1*0)= (-1,0). If we identify (0,1) with i (having dodged the question of how to distinguish between roots), we can write any complex number as (a, b)= a+ bi and have i*i= (-1,0)= -1.
 

Want to reply to this thread?

"What is complex number" You must log in or register to reply here.

Related Threads for: What is complex number

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top