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Math Help - Complex number or function

  1. #1
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    Complex number or function

    I have a question that may seem strange and may not even make sense. Suppose I have a function f(x)=1/x. Now let's say I'm working in the complex plane and I want to plot this curve with f(x) being the imaginary axis. Is the following:

    C=x+i*1/x

    considered a complex number or a function (I could make the f(x) curve by computing C for all x)? Does the notation C(x)=x+i*1/x make sense if it is a function?

    Thanks.
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  2. #2
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    Re: Complex number or function

    Quote Originally Posted by claforet View Post
    I have a question that may seem strange and may not even make sense. Suppose I have a function f(x)=1/x. Now let's say I'm working in the complex plane and I want to plot this curve with f(x) being the imaginary axis. Is the following:
    C=x+i*1/x
    considered a complex number or a function (I could make the f(x) curve by computing C for all x)? Does the notation C(x)=x+i*1/x make sense if it is a function?
    If z complex variable the \frac{z+i}{z}\text{ or } z+\frac{i}{z} are both complex function.

    As a matter of custom x~\&~y are used as real variables.
    But that said \frac{x+i}{x}\text{ or } y+\frac{i}{y} are both complex function because of the \bf{i}
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    Re: Complex number or function

    So if x is real and x+i*1/x is a complex function, is the notation:

    C(x)=x+i*1/x correct (i.e. is C(x) allowed if x is not a complex variable?)
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    Re: Complex number or function

    Quote Originally Posted by claforet View Post
    So if x is real and x+i*1/x is a complex function, is the notation:
    C(x)=x+i*1/x correct (i.e. is C(x) allowed if x is not a complex variable?)
    Well of course f(x,y)=x+2yi where x~\&~y are real variables is perfectly good complex function.
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