Let Z=x+iy then we have
So
Now z +
Let P(x,y) represent the complex number Z=x+iy in the complex plane(Argand plane) and let O(0,0) be the origin
Then we have OP=
Here Z=1+i so that P(x,y)=P(1,1)
Hence OP=
If is a cube root of unity , then upto 2n factors is
We have any line of the form x=a constant is a line parallel to Y-axis.
which is purely imaginary number.
Also when y=0, the number will become zero