Question

Statement I Every complex number $z=x+i y$ corresponds to the ordered pair $(x, y)$ and can be represented as unique point $(x, y)$ in the $x y$-plane.
Statement II The plane having a complex number assigned to each of its point is called the complex plane or Argand plane.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Neither I nor II is true

Answer 1

Answer: (C)

We already know that corresponding to each ordered pair of real numbers $(x, y)$, we get a unique point in the $x y$-plane and vice-versa with reference to a set of mutually perpendicular lines known as the $X$-axis and the $Y$-axis. The complex number $x+i y$ which corresponds to the ordered pair $(x, y)$ can be represented geometrically as the unique point $P(x, y)$ in the $x y$-plane and vice-versa.

Some complex numbers such as $2+4 i,-2+3 i, 0+1 i$ $2+0 i,-5-2 i$ and $1-2 i$ which correspond to the ordered pairs $(2,4),(-2,3),(0,1), \quad(2,0), \quad(-5,-2)$ and $(1,-2)$ respectively, have been represented genmetrically by the points $A, B, C, D, E$, and $F$ respectively in the plane having a complex number assigned to each of its point is called the complex plane or the Argand plane.