Complex Numbers
Definition: A complex no. is defined as, z = a + bi, a and b are real numbers.
The real part of z, denoted by Re(z), is Re(z) = a
the imaginary part of z, denoted by Im(z), is Im(z) = b
i is defined as the square root of -1. i.e. i = sq rt(-1)
z = a + bi is known as the Cartesian form
We can draw a complex number on a diagram called Argand diagram.
Graphs are drawn on a Cartesian plane(Cartesian diagram) with x-y axis.
Argand diagrams are like the Cartesian diagram. Instead of the x-axis, we have the real axis, R and instead of the y axis, we have the Imaginary axis, I.
The modulus of the complex number Z = 2 + i is the lenght of the line segment from O to A.
Notation for the modulus of Z is | Z |. From the diagram above, | Z | = sq rt( 2^2 + 1^2) = sqrt(5).
