Complex question help (1 Viewer)

[greenlemings]

Geometrical Properties
If |z|=1, where z is a positive number,
RTS: arg (z+1)= half of arg (z)

 

[Drongoski]

z therefore lies on a circle, centred at the origin, radius 1. If you draw this unit circle, and for convenience of illustration, pick any point z, say P, on the circle, in the 1st quadrant. The complex number 1 is where the circle cuts the x-axis, at Q say, on the right. With the 3 vertices, the origin O, the points P and Q form 3 points of a parallelogram OPQR. Then R represents z+1. Because OP = OQ, OPQR is in fact a rhombus. So OR bisects angle POQ; i.e. arg(z+1) = half of arg z.

You may want to show when z lies elsewhere: the other quadrants.

 

[greenlemings]

ah okay I got it. Thanks so much ^_^