# Complex number or function

• Dec 7th 2011, 12:23 PM
claforet
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.
• Dec 7th 2011, 12:38 PM
Plato
Re: Complex number or function
Quote:

Originally Posted by claforet
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 $\displaystyle z$ complex variable the $\displaystyle \frac{z+i}{z}\text{ or } z+\frac{i}{z}$ are both complex function.

As a matter of custom $\displaystyle x~\&~y$ are used as real variables.
But that said $\displaystyle \frac{x+i}{x}\text{ or } y+\frac{i}{y}$ are both complex function because of the $\displaystyle \bf{i}$
• Dec 7th 2011, 12:43 PM
claforet
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?)
• Dec 7th 2011, 12:54 PM
Plato
Re: Complex number or function
Quote:

Originally Posted by claforet
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 $\displaystyle f(x,y)=x+2yi$ where $\displaystyle x~\&~y$ are real variables is perfectly good complex function.