Complex numbers: don't understand graph of 1/z

[james5]

1/z is 1/(x+iy)

however, i then multiply by the complex conjugate and get:

(x-iy)/(x^2+y^2)

now, how do i graph this?

thanks.

 

[d_leet]

What are you trying to graph? x versus y or what?

 

[lotrgreengrapes7926]

To fully graph it, you would need a 4-dimensional graph, with axes $$x,y,a,b$$, so that $$x+y\imath=\frac{1}{a+b\imath}$$.
You could have 2 3-D graphs, $$z=\Re\left({\frac{1}{x+y\imath}}\right)$$ and $$z=\Im\left({\frac{1}{x+y\imath}}\right)$$.

 

[james5]

well, i think it's not that complex since the graph i made that is correct is just one that goes down diagonally... so, it's basically the graph of x-iy since x^2 and y^2 are basically a whole number...

 

[HallsofIvy]

well, i think it's not that complex since the graph i made that is correct is just one that goes down diagonally... so, it's basically the graph of x-iy since x^2 and y^2 are basically a whole number...

Perhaps it would be better if you explain what you are talking about! What do you mean by "basically a whole number"? And, as you were asked before, what exactly are you graphing?