Math wizards: Is a complex number considered a real number????

[poohbear2]

I know that a complex number is made up of a real number and an imaginary number, but is the whole complex number considered a real number????

 

[lvs_eeyore]

Dh is pretty good at math but is confused by your explanation. Can you give an example of what you mean?

 

[LindaG4458]

DH says it is neither real nor imaginary - the only description of the entire number is complex.

 

[poohbear2]

LindaG4458:

So even though you can graph, add, multiply complex numbers, its still not considered a real number? Interesting..... Thanks!

lvs_eeyore:

A complex number is made up of a real number ( a) and a number that is not considered real (b) which is a negative square root.

So a+bi is considered a complex number, where a is maybe 4 and bi is maybe 2i (4+2i).

 

[Rokkitsci]

Imaginary numbers were "invented" so that mathemeticians could continue analyses that required taking the square root of a negative number. This operation is not possible in the "real" world, because any number multiplied by itself always produces a positive number, regardless of whether the original number is negative or not. Therefore square roots of negative numbers do not exist in the "real" world.

They are by definition not "real" numbers, so therefore any representation that contains an imaginary number is also not a real number.

If a number has a real part and an imaginary part it is called a complex number.

The letter "i" was chosen to represent the imaginary portion of a complex number.

The definition of "i" mathematically is = Square root of negative 1.

Therefore, "i" squared = negative one,

and "i" to the fourth power gets you back to positive one again.

So - any number "N" can be represented by the complex notation:

N = a + bi

where "a" is the real portion and "b" is the imaginary portion and "i" has the value = "square root of negative one."

"Real numbers" is the subset of all numbers where the value of "b" = 0.

This topic is normally addressed in high school Algebra during a student's third year of mathematics.

Once inventied by mathematicians, physicists, engineers, statisticians, (and others) found many applications for the use of complex numbers in their analysis of "real world" situations.

For instance, the study of electromagnetics would be (nearly) impossible without the use of complex number notation.

Complex numbers provide a very consise methodology for analysis of conic curves and other physical phenomena.

etc etc - thousands of applications.

hope this helps.

I never thought I would encounter a question about complex numbers on a Disney Board. Thanks

 

[poohbear2]

WOW! Thanks for the great response!

I hope I made your day...