Question

I honestly don't understand what im being asked to show or how to show it. Give a geometric interpretation of why z x z* is a real number

Answer 1

Umm umm umm um

Answer 2

For some point z, here is one way to get there,\[\large\rm z=r e^{i \theta}\]\[\large\rm z^*=re^{-i \theta}\]Agree with the above?
So the product,\[\large\rm z\cdot z^*=r^2 e^{i(\theta-\theta)}=r^2\]Oh that's not really geometric is it -_- Hmm.

So like.. you're spinning in one direction, and going radially outward to the point,
and then you're spinning back the same angular distance and going radially outwarrrrrrrrrrrrd... mmm nah that's not exactly the explanation I was hoping to make.. hmm

Answer 3

exactly doing this algebraically is cake. i dont understand the geometric part so im trying to draw a graph.

Answer 4

this is what i was doing... im trying to make the point that subtracting the angles with give no angle and then the only thing left is the positive x axis and zero degrees on the real number line... im confusing myself

Answer 5

ooo ya i like the way you're doing it :O
that makes sense to me.
The product gives us an angle of 0,
and the square of the radial length.