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

I just started to look at complex numbers.

Prove the ``Parallellogram law''

http://www.sosmath.com/complex/number/complexplane/img4.gif

This is how I solved it:

[tex]z=a+bi[/tex]

[tex]w=c+di[/tex]

[tex]|z+w|^2=\sqrt{(a+c)^2+(b+d)^2}=a^2+2ac+c^2+b^2+2bd+d^2[/tex]

then we have

[tex]|z-w|^2=\sqrt{(a-c)^2+(b-d)^2}=a^2-2ac+c^2+b^2-2bd+d^2[/tex]

[tex]2(|z|^2+|w|^2)=2((a^2+b^2)+(c^2+d^2)) = 2a^2+2b^2+2c^2+2d^2[/tex]

[tex]a^2+2ac+c^2+b^2+2bd+d^2+a^2-2ac+c^2+b^2-2bd+d^2=2a^2+2b^2+2c^2+2d^2[/tex]

My question is:

Was my calculation OK or was it a misscalculation (a lucky one which prooved the formula)

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

Dismiss Notice

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!

# Complex numbers + proof

Loading...

Similar Threads - Complex numbers proof | Date |
---|---|

I Dividing Complex Numbers | Jan 21, 2018 |

B Complex products: perpendicular vectors and rotation effects | Dec 17, 2017 |

Proof of trigonometric multiplication of complex numbers | Oct 24, 2010 |

Complex number proof | May 11, 2007 |

Complex number proof | Mar 16, 2007 |

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