hi,

'Find all the solutions of z bar= z^3 in cartesian form ?', thanks in advance for any help

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- Mar 29th 2009, 07:40 AMspeckmagooequation involving complex numbers
hi,

'Find all the solutions of z bar= z^3 in cartesian form ?', thanks in advance for any help

- Mar 29th 2009, 07:56 AMrunning-gag
- Mar 29th 2009, 08:26 AMspeckmagoo
hi thanks for ur assistance!!, id really appreciate if you could explain a little further as im not quite understanding how to go about using the approach u suggested, cheers

- Mar 29th 2009, 09:03 AMrunning-gag
Let $\displaystyle z = r\:e^{i\theta}$

$\displaystyle r\:e^{-i\theta} = r^3\:e^{3i\theta}$

leads to $\displaystyle r = r^3$ and $\displaystyle 3\theta = -\theta +2k\pi$

$\displaystyle r = r^3$ is solved by $\displaystyle r \:(r^2-1)=0$ which leads to $\displaystyle r=0$ or $\displaystyle r=1$

$\displaystyle 3\theta = -\theta +2k\pi$ leads to $\displaystyle \theta = k\:\frac{\pi}{2}$

The solutions are therefore $\displaystyle z=0, z=1, z=i, z=-1, z=-i$ - Mar 29th 2009, 12:30 PMspeckmagoo
hi,

thanks for ur assistance again, it now makes more sense, thanku