
Complex analysis help
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 =$\displaystyle r.e^{(i.\theta)}$
and i.z = $\displaystyle 1.e^{(i.(\pi/2))} . r.e^{(i.\theta)}$
therefore = $\displaystyle r.e^{i(\theta + \pi/2)}$
and as the argument here has been shifted by pi/2 the second point is perpendicular from the first?

That looks correct! However, don't forget that you can rotate by any multiple of 2 pi and still you will get the same answer.

Cheers,
Was unsure if the way i represented i was ok,