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Math Help - Find the Argument

  1. #1
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    Find the Argument

    Find the Argument of the following.

    Arg\left[cis\left(2pi/3\right)cis\left(pi/4\right)/cis\left(-pi/6\right)cis\left(3pi/4\right)\right]
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  2. #2
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    Do you mean...

    \displaystyle \textrm{Arg}\,{\left[\frac{\textrm{cis}\,{\left(\frac{2\pi}{3}\right)\,  \textrm{cis}\,{\left(\frac{\pi}{4}\right)}}}{\text  rm{cis}\,{\left(-\frac{\pi}{6}\right)}\,\textrm{cis}\,{\left(\frac{  3\pi}{4}\right)}}\right]}?

    If so, simplify the stuff in the big square brackets first.
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  3. #3
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    When multiplying you add the angles. When dividing you subtract the angles. Finally if your angle is not between -\piand \pi, add or subtract a multiple of 2\pi to get an angle that is.
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  4. #4
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    Maybe start by simplifying the term inside the argument using

    \displaystyle z_1\times z_2 = r_1\times r_2 (\cos(\theta_1+\theta_2 ) +i \sin(\theta_1+\theta_2 ) )

    and

    \displaystyle \frac{z_1}{z_2} = \frac{r_1}{ r_2} (\cos(\theta_1-\theta_2 ) +i \sin(\theta_1-\theta_2 ) )
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