Given $ z = -1 - i$ ,I converted it to polar form, resulting r =$\sqrt 2$.
And $\theta = \tan^{-1} (\frac{-1}{-1}$) = 0.785 rads, which seems incorrect with the solutions of my instructor I don't understand why...
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2 Answers
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Hint:
In which quadrant of the plane does that point reside?
answered Mar 23, 2016 at 19:22
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$\begingroup$ 3rd, therefore i'd subtract the result from $\pi$ $\endgroup$– PupilMar 23, 2016 at 19:26
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$\begingroup$ @XCIX: Why? What are the reasonable values for $\theta$ in the 3rd quadrant? $\endgroup$ Mar 23, 2016 at 19:28
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$\begingroup$ @Henrik the result is -2.356, that is a possible value(and turned to be correct with the solution) $\endgroup$– PupilMar 23, 2016 at 19:35
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$\begingroup$ You really should express those angles as multipla of $\pi$ (but that of course requires that you know those values of $\sin$/$\cos$/$\tan$), those numbers mean nothing to me (but I can do the calculations needed to compare). $\endgroup$ Mar 23, 2016 at 19:46
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$-1-i$ is in the 3rd quarant, reasonable values for $\theta$ are between $\pi$ and $\frac32\pi$ (or $-\pi$ and $-\frac\pi2$ if you prefer values between $-\pi$ and $\pi$). $\tan^{-1}$ gives values between $-\frac\pi2$ and $\frac\pi2$, so you need to correct it by either adding or subtracting $\pi$.
answered Mar 23, 2016 at 20:02
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