# complex numbers argand diagram

• Feb 23rd 2011, 12:38 AM
kumquat
complex numbers argand diagram
If, with an Argand diagram with origin O, the point P represents z and Q represents 1/(conjugate of z), prove that O, P and Q are collinear and find the ratio OP:OQ in terms of |z|.

ive tried letting z = x + iy so that P = (x + iy) but i havnt got far totally stuck
• Feb 23rd 2011, 02:21 AM
DrSteve
Try letting $z=re^{i\theta}$.
• Feb 23rd 2011, 02:41 AM
kumquat
ok that worked really well i used z = r cis (theta) and i proved the angle the complex numbers make is the same so therefore collinear, but i do not understand how to find the ratio OP:OQ in terms of |z|
• Feb 23rd 2011, 02:45 AM
DrSteve
|z|=r. Does that help?