Consider a real number in two dimensional plane that X axis and Y axis having ordered pair : P(x,y) or (3,4).
To find it's absolute value we will find it's Distance from origin.
As Coordinate of Origin = (0,0)
Absolute Value of OP = [tex]\left | OP \right |[/tex]
= [tex]\sqrt{(0-x)^2+(0-y)^2}=\sqrt {x^2+y^2}[/tex]
If the point is Q(3,4)
[tex]\left | OQ \right |=\sqrt{3^2+4^2}=\sqrt{5^2}=5[/tex]
In case of a complex number :
Z = a + bi , we consider two axes Real Axis and Imaginary Axis.
We represent Z that is (a,b) in the same way that we represent point in two dimensional plane.
To find it's absolute value , we will find it's distance from origin.
[tex]\left | Z \right |= \sqrt{a^2+b^2}[/tex]
If [tex]Z_{1}[/tex] = 6 + 8 i
[tex]\left | Z_{1}\right |=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]
