complex nos have an analogy with points on cartesian coordiantes.So how it is that (x,y) gets converted into x+iy.i know all those derivations that i*y gives complex no.(A point on y axis), but why the plus sign in between intead of ",". what is its significance. Is it adding of complex no. to real no.(makes no sense) or anything else, why notminus"-"?

Hi twesh,

A complex number can be viewed as a point or "Position Vector" in "a" two-dimensional Cartesian Coordinate "system" called the "Complex Plane" or Argand diagram. Here the point to note is :

The Argand Plane is a    """"2D Cartesian Coordinate System"""" that has been created , in order to conduct operations on complex numbers graphically.

Now (x,y) is coordinate of a point in a "2D Cartesian Coordinate System" that has x- and y- axes both of real numbers.

Now to visualise Complex Number Operations Graphically, we create another "2D Cartesian Coordinate System", that has x-axes as the real numbered axes, and y-axes as the imaginary numbered axes,

Hence the coordinates of any point on this plane, in this system, "called the Argand Plane", the co-ordinates of a point are not(x,y) BUT (x,iy)

"the real axis and the orthogonal imaginary axis"

Complex Plane is "a modified Cartesian Plane"

And another characteristic that we, the creators of this Argand plane, assign to this Plane is that Position "vectors" are not (x)i + (iy)j

BUT "x+iy".

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In this Case, Remember that : First we had the complex numbers 2+3i

And Then,

We created the Argand Plane(a 2D Cartesian System) to visualise their opeations like additions and multiplication, etc.

While creating this Argand Plane, we assigned it a few characteristics that were needed in relation to complex numbers.

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The Definition:

The concept of the complex plane allows a geometric Interpretation of Complex Numbers. Under addition, they add like Vectors. The multiplication of two complex numbers can be expressed most easily in polar Coordinates – the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.

Regards,

Rajat

Askiitians Expert