Thread: complex numbers argand diagram

1. 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

2. Try letting $z=re^{i\theta}$.

3. 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|

4. |z|=r. Does that help?