How to demostrate the associative property of adittion? (for complex numbers)

Question

amistre64 · Answer

sin(a+b) = sin(a)cos(b) + sin(b)cos(a)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

might be useful

osanseviero · Answer

Isn't there a simpler way?

amistre64 · Answer

hmm, can we use the vector properties of complex numbers?  then address that vector addition is associative?

amistre64 · Answer

a complex number (a+bi) can be expressed as a vector (a,b)

amistre64 · Answer

take 3 vectors, u,v,w

(u+v) + w

and show that you can convert it to u + (v+w)

osanseviero · Answer

Ok...That is what I was thinking to do

osanseviero · Answer

Do I put them as points or vectors, then?

amistre64 · Answer

a + bi
+ c + di
--------
 a+c + (b+d)i


 a+c + (b+d)i
  m   +    ni
-------------
(a+c+m) + (b+d+n)i

or some other convoluted torture lol

amistre64 · Answer

vectors is best, since its a pretty basic notion to show that vector addition is associative

osanseviero · Answer

So...what? I do the same drawing two times?

amistre64 · Answer

http://www.rootmath.org/linear-algebra/algebraic-properties-of-vectors about 3:30 starts the associative proofing of vectors

osanseviero · Answer

I am trying commutative for myself, but thanks :) this will help

amistre64 · Answer

yep, good luck

osanseviero · Answer

thanks

osanseviero · Answer

How to demostrate that z+(-z)=0 ?