Complex number argument (1 Viewer)

juantheron · Feb 23, 2013

Question::

If $z = \cos \theta + i.\sin \theta$ . Then prove that

(1) $\displaystyle \arg(z^2+\bar{z}) = \frac{\arg(z)}{2}\;\;,$ If $\displaystyle 0 \leq \theta <\frac{\pi}{3}\;\;,\pi < \theta <\frac{5\pi}{3}$

(2) $\displaystyle \arg(z^2+\bar{z}) = \pi+\frac{\arg(z)}{2}\;\;,$ If $\displaystyle \frac{\pi}{3} < \theta < \pi \;\;,\frac{5\pi}{3} < \theta < 2\pi$

(3) $\displaystyle \arg(z^2+\bar{z}) = 0\;\;,$ If $\displaystyle \theta = \frac{\pi}{3} \;,\pi\;,\frac{5\pi}{3}$

jyu · Feb 26, 2013

juantheron said:
Question::

If $z = \cos \theta + i.\sin \theta$ . Then prove that

(1) $\displaystyle \arg(z^2+\bar{z}) = \frac{\arg(z)}{2}\;\;,$ If $\displaystyle 0 \leq \theta <\frac{\pi}{3}\;\;,\pi < \theta <\frac{5\pi}{3}$

(2) $\displaystyle \arg(z^2+\bar{z}) = \pi+\frac{\arg(z)}{2}\;\;,$ If $\displaystyle \frac{\pi}{3} < \theta < \pi \;\;,\frac{5\pi}{3} < \theta < 2\pi$

(3) $\displaystyle \arg(z^2+\bar{z}) = 0\;\;,$ If $\displaystyle \theta = \frac{\pi}{3} \;,\pi\;,\frac{5\pi}{3}$

juantheron · Mar 21, 2013

Thanks jyu

Complex number argument (1 Viewer)

juantheron

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