# Why the point of x + iy would be (x, y) ?

1. Sep 22, 2009

### I_am_no1

What argand diagrams really are ? Is there any differance between graph and argand diagram?

For complex number i is a sign that is count as $$\sqrt[]{-1}$$
Then why the point for a + ib would be (a, b) in argand diagram ?

That means, x = real part = a
y = imaginary part = b
so if i want to find out real numbers point than it would be on x axis alone, right? [would the point for 'a' (a € Real number) would be (a, 0) in argand diagram ?]

2. Sep 22, 2009

### pbandjay

I just think of it as a matter of notation. To develop the ordered pairs of real numbers, define an addition and multiplication on R^2:

(a,b) + (x,y) = (a+x, b+y)
(a,b) * (x,y) = (ax-by, bx+ay)

According to this definition, (0,1)*(0,1) = (-1,0) and is then denoted i^2 by construction. Rewriting (a,b) as a+bi and calling the plane C rather than R^2, the operations hold:

(a+bi) + (x+yi) = (a+x) + (b+y)i
(a+bi) * (x+yi) = (ax-by) + (ay+bx)i

And if b=0 in a+bi then a+0i = a which is the real part of the complex number and is a real number, also known as (a,0) in C.

Last edited: Sep 22, 2009
3. Sep 22, 2009

### tiny-tim

Hi I_am_no1!

(have a square-root: √ )
Not really …

a complex number can be written in standard form as a + ib, or in polar form as re, and they correspond to cartesian and polar coordinates on an argand diagram.
Yes, the x axis is all the real numbers, and the y axis is all the imaginary numbers …

for that reason, they're also called the real axis and the imaginary axis.