Algebraic Structure of Complex Numbers

Let us learn Algebraic structure of complex numbers,

When you come to quadratic equations you will be confronted with an entity (or non-entity) whose name is written this way - √-1, and pronounced "square root of minus one."

Complex numbers are points in the plane endowed with additional structure. We consider the set R2 = {(x, y): x, yR}, i.e., the set of ordered pairs of real numbers. Two such pairs are equal if their corresponding components coincide:

(x1, y1) = (x2, y2) iff x1 = x2 and y1 = y2.

With two operations - addition and multiplication - defined below, the set R2 becomes the set C of complex numbers. R2 considered as a set of complex numbers C is called Argand diagram or Argand plane or Gauss plane.

Hope the above explanation helped you.