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 | Science Articles, Homework Help, Discussion**

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

**Physics Forums | Science Articles, Homework Help, Discussion**