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Math Help - graphing imaginary numbers

  1. #1
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    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?
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  2. #2
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    Graphing complex numbers use a Real-Imaginary plane.

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

    if so f(x) =\sqrt{x}, x\in [0,\infty)
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  3. #3
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    Argand's diagram

    Quote Originally Posted by holly47 View Post
    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.
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  4. #4
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    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 y= \sqrt{x}, with x real, y is real for x\ge 0, pure imaginary for x< 0. So for x\ge 0 you will have just the graph of 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 z= \sqrt{|x|} in the xz- plane.
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