Am doing some problems on complex analysis and am having some trouble getting my head around some of the basic points.

If z represents a point R on the complex plane,

and I take i . z to give another point T , then the line segment OT will be perpendicular to OR.

to show this is true is the following correct?

z = x +yi =

and i.z =

therefore =

and as the argument here has been shifted by pi/2 the second point is perpendicular from the first?