0
$\begingroup$

I can understand how a complex numbers such as $10 + 7i$ can be plotted in complex plane with Imaginary and Real axis. But I have no idea how to approach this problem. I have been asked to plot $e^{(0.12+i) \theta\ } $.

I cannot understand what is the role of $ \theta\ $ in this equation. I also do not know how I can raise the power of Euler constant to a complex number. I appreciate any hint, comment, clue, reference, etc to solve this problem.

$\endgroup$
3
$\begingroup$

Hint : $e^{i\theta}=\cos\theta + i \sin\theta$

Parametric form of circle $(r\cos\theta,r\sin\theta)$

$\endgroup$
1
$\begingroup$

Split it: $e^{(a+i)\theta}=e^{a\theta}e^{i\theta}$. Use the Awesome Hint to see that the product contains an exponentially growing and a oscillating part...

$\endgroup$
  • 1
    $\begingroup$ The Awesome Hint... I see what you did there... :P $\endgroup$ – evil999man Mar 13 '14 at 7:11
  • $\begingroup$ "Awesome hint" +1 $\endgroup$ – Guy Mar 13 '14 at 7:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.