Inverse of z
Using , geometrically show how you would construct .
NOTE z* means the conjugate of z.
I have no idea. I know how to show it algebraically, since we'd have:
Then, multiply the left side by the complex conjugate and we get the right hand side...
How'd I show this geometrically?
Plot the point z on a graph.
Reflect that point in the real axis; that is z conjugate.
Now divide by the absolute value of z squared.
How do you "divide" something on the graph...
Originally Posted by Plato
So if we have our axis', we'd have:
ib on the vertical axis (above 0)
-ib on the vertical axis (below 0)
And we'd have a somewhere on the traditional x-axis (greater than 0)
So then a - ib will put us in the 4th quadrant, and that is our conjugate...
How do I graph a^2 + b^2 and then divide this by the point I already created from the conjugate?
i suppose you divide the co-ordinates of the reflected point by the quantity a^2 + b^2
Originally Posted by Ideasman
No idea how. I don't even know what my "b" is. It'd have to be "ib," no? A diagram would be helpful, but probably too hard to do on here.