Let(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

F=z_1\cos\theta_1\cos\theta_2+z_2(e^{i\alpha_1}\sin\theta_1\cos\theta_2+e^{i\alpha_2}\cos\theta_1\sin\theta_2)+z_3e^{i(\alpha_1+\alpha_2)}\sin\theta_1\sin\theta_2

[/tex]

where [tex] 0\le\alpha_i\le\pi,~0\le\theta_i\le\pi/2 [/tex] and [tex] z_i[/tex]

are some fixed complex numbers.

Then how to find

[tex]\max_{\theta_i, \alpha_i}|F|[/tex]

We note that [tex]|F|\le1[/tex].

Particularly, I want to know if there is any set of constraints like the case of optimization over real variables. [I know definitely that the conditions are [tex] \theta_1=\theta_2; \alpha_1=\alpha_2[/tex]. But I have to establish it. So, how to prove it?]

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Maxima problem

Loading...

Similar Threads - Maxima problem | Date |
---|---|

Setting Up the Domain for Maxima/Minima Word Problems | Mar 24, 2013 |

Advanced Lagrange Maxima Minima Problems | Dec 18, 2012 |

Maxima and minima problem | Aug 6, 2012 |

Maxima-Minima for a 6 independent variable problem | Jul 29, 2009 |

Maxima-minima problems | Dec 17, 2004 |

**Physics Forums - The Fusion of Science and Community**