0
$\begingroup$

Use the rules for multiplication of two complex numbers written in the form $r(\cos\theta +i\sin\theta)$ to show that $\sin(\theta_1 +\theta_2)=\sin\theta_1\cos\theta_2 +\sin\theta_2\cos\theta_1$ and $\cos(\theta_1 +\theta_2)=\cos\theta_1\cos\theta_2 −\sin\theta_1\sin\theta_2$.

I have no idea how to do this. It's part of a complex number worksheet but I can't find a way to do it. I thought about using Euler's formula but got no where. Thank you in advance

$\endgroup$
  • $\begingroup$ If you already know that $\sin x = \frac{e^{ix} - e^{-ix}}{2i}$ and $\cos x = \frac{e^{ix}+e^{-ix}}{2}$ then the rest is just grouping thing. $\endgroup$ – Stephen Dedalus Dec 16 '13 at 12:52
  • $\begingroup$ @Baranovskiy: I don't think that's what she's supposed to do here. Simply multiplying $e^{i\theta_1}$ with $e^{i\theta_2}$ will do. $\endgroup$ – Henning Makholm Dec 16 '13 at 12:53
  • $\begingroup$ @HenningMakholm I misunderstood question but after editing I can see that you are right. $\endgroup$ – Stephen Dedalus Dec 16 '13 at 13:00
0
$\begingroup$

$\exp(i\theta_1)\exp(i\theta_2)=\exp i(\theta_1+\theta_2)=\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2)=(\cos(\theta_1)+i\sin(\theta_1)\dot{}(\cos(\theta_2)+i\sin(\theta_2)$

bacause you have: $\exp(i\phi)=cos(\phi)+i\sin(\phi)$

$\endgroup$

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.