# graphing imaginary numbers

• Aug 9th 2010, 02:19 PM
holly47
graphing imaginary numbers
ok. My teacher wants our class to graph (*being sq root) f(x)=*x . And we have to have some negatives. which means there will be imaginary numbers. so how do you graph those?
• Aug 9th 2010, 02:25 PM
pickslides
Graphing complex numbers use a Real-Imaginary plane.

I think you want to graph the function on the x-y plane?

if so $\displaystyle f(x) =\sqrt{x}, x\in [0,\infty)$
• Aug 9th 2010, 04:04 PM
wonderboy1953
Argand's diagram
Quote:

Originally Posted by holly47
ok. My teacher wants our class to graph (*being sq root) f(x)=*x . And we have to have some negatives. which means there will be imaginary numbers. so how do you graph those?

I would suggest Googling "Argand's diagram" to see what it would look like.
• Aug 10th 2010, 02:24 AM
HallsofIvy
Are you sure you have understood the directions correctly? Just graphing a complex number, a+ ib, requires two dimensions. Graphing a function, y= f(x), where both x and y are complex numbers, requires two dimensions for both variables- you would need a four dimensional graph! If you take x to be real only, you would need a three dimensional graph which is at least possible. If you take the x-axis to be the real x variable, you can let the y-axis be the real part of f(x), and the z axis be the imaginary part.

Now for $\displaystyle y= \sqrt{x}$, with x real, y is real for $\displaystyle x\ge 0$, pure imaginary for x< 0. So for $\displaystyle x\ge 0$ you will have just the graph of $\displaystyle y= \sqrt{x}$ in the xy-plane. For x< 0, [tex]\sqrt{x}= \sqrt{-1|x|}= i\sqrt{|x|}. The graph will be turned 90 degrees at x= 0 and will be the graph of $\displaystyle z= \sqrt{|x|}$ in the xz- plane.