Just want to share this neat idea for why $-\times-=+$

Question

karatechopper · Answer

oh oh oh go I'm listening! :D

anonymous · Answer

spit that fire

ganeshie8 · Answer

let $r_1$ and $r_2$ be two positive numbers, then :

$$\large (-r_1)(-r_2) = (r_1e^{i\pi})(r_2e^{i\pi})=r_1r_2e^{i2\pi}=r_1r_2$$

anonymous · Answer

neat idea, thanks

ikram002p · Answer

that wouls also explain why -×+=- 
i loved it

ganeshie8 · Answer

didn't want to add anything as it looks so elegant+complete as an one liner xD
But here some explanation :

To multiply two complex numbers, we simply "multiply the two lengths" to get the resulting length and "add the two angles" to get the resulting angle.

$$(r_1,\theta_1)*(r_2,\theta_2)=(r_1r_2,~\theta_1+\theta_2)$$

Next notice that the angle for any negative number is $\pi$ as they fall on the negative real axis. Consequently, multiplying two negative numbers adds up the angles$(\pi+\pi)$ taking the result to positive real axis.