#### Topic: Function...with use of the real, imaginary, and complex values

Why not add support for real, imaginary, and complex values? Even naturally undefined values.
Examples:
[All real] Cos(x+y) = Cos(x)Cos(y)-Sin(x)Sin(y)
[Complex] Cos(x+iy) = Cos(x)Cosh(y)-i*Sin(x)Sinh(y)
[Imaginary] Cos(ix+iy) = Cos(i{x+y}) = Cosh(x+y) = Cosh(x)Cosh(y)+Sinh(x)Sinh(y)

Here is a list of current complex valued functions that I have obtained:

Ln(x+iy) = {Ln(x^2+y^2)+i*arctan(y/x)}/2 = {Ln(x^2+y^2)+i*arccot(x/y)}/2
Cos(x+iy) = Cos(x)Cosh(y)-i*Sin(x)Sinh(y)
Sin(x+iy) = Sin(x)Cosh(y)+i*Sinh(y)Cos(x)
Tan(x+iy) = [Tan(x)+i*Tanh(y)]/[1-i*Tan(x)Tanh(y)]
Cosh(x+iy) = Cosh(x)Cos(y)+iSinh(x)Sin(y)
Sinh(x+iy) = Sinh(x)Cos(y)+i*Sin(y)Cosh(x)
Tanh(x+iy) = [Tanh(x)+i*Tanh(y)]/[1+i*Tanh(x)Tan(y)]
e^(x+iy) = e^(x)*{Cos(y)+i*Sin(y)}
(x+iy)^(n) = (x^2+y^2)^(n/2)*(Cos[n*arctan{y/x}]+iSin[n*arctan{y/x}]) [For all real, imaginary, and complex values of n...I recommend it when n is negative value or a fraction]

If it helps, I would note that I didn't put any functions that don't have imaginary values. This is because I am aware that the code can read it in a way that does all 3 at once. Say for example I have a definite value that I am plugging into the function:
Cos(3) <-- this looks like it is only real, however I am certain you can write it such that it reads it as Cos(3+0i) because it will be read the exact same in mathematical terms:
Cos(3+0i) = Cosh(0)Cos(3)+iSin(3)Sinh(0) = Cos(3)
Making the code read all three simultaneously will help reduce the amount of work needed.

I am still working on deriving the inverses...they are miserable so far...but I will eventually derive them from the rules that I have above. I am willing to help in any way I can because this is the best graphing software I have found so far, and I am willing to invest time to help improve it in any way I can.

#### Re: Function...with use of the real, imaginary, and complex values

After reading multiple posts, I see that the developer is busy, is there some way I can help with Graph? I don't know code, but if I need to I am willing to learn code to help an excellent program.

#### Re: Function...with use of the real, imaginary, and complex values

Graph already supports complex numbers in calculations. To use complex numbers when plotting however, you need to enable Calculate with complex numbers under the Settings tab in theEdit|Axes dialog.

#### Re: Function...with use of the real, imaginary, and complex values

I see this, but would it be possible to continually support real, imaginary, and complex values without needing to enable or disable it? As you have seen, I have given functions that hold true for real, imaginary, and complex numbers simultaneously [With the exception of Ln(x+iy) if x = 0 therefore making it ln(y) + i*Pi/2] Where i can be treated as a special coefficient instead of the original idea of sqrt(-1).

I would like to know if it can be treated as a special coefficient instead of a number for calculations.

#### Re: Function...with use of the real, imaginary, and complex values

Can you clarify what exactly it is you are trying to do? I think Graph can already do it, but I am having trouble figuring out what it is you want to do.

#### Re: Function...with use of the real, imaginary, and complex values

Okay, in general: I would like to provide you with functions that will do all three numbers. Real, imaginary, and complex numbers. This way I do not need to turn on the "imaginary" part of graph. It would be of great convenience to be able to graph real and imaginary simultaneously from a single function such as e^[x+ix] = e^(x)*[Cos(x)+iSin(x)] instead of needing to create two separate graphs to graph one version that abides by one rule.

For example: [x is the variable and y can be a constant] Cos(x+iy) = Cos(x)*Cosh(y)-i*Sin(x)*Sinh(y). If it is possible, it would be nice (although I am aware you have been a bit too busy to update and improve graph) to plug in one function of any of the three types of numbers and that graph will plot it automatically, regardless of whether it is real, imaginary, or complex because it will produce the correct answer every time instead of having to write more rules for "if real then this", "if imaginary then this", or "if complex then this" when you can have it read for a real and imaginary number simultaneously and then merely plug in those values. An example is like this, the computer could be looking for the specific complex number 1+i however the input is 3+4i, the computer can then read that the real is 3 and that the imaginary is 4 and then plug them into corresponding equation:

Cos(3+4i) = Cos(3)*Cosh(4)-i*Sin(3)Sinh(4)
Compared to:
Cos(x+iy) = Cos(x)*Cosh(y)-i*Sin(x)*Sinh(y)
See? Instead of needing to worry about that unusual imaginary part, you only need to use the corresponding relation instead and it also holds for the cases of just real and just imaginary also:
Cos(3+0i) = Cos(3)*Cosh(0)-iSin(3)*Sinh(0) = Cos(3)
Cos(0+4i) = Cos(0)*Cosh(4)-iSin(0)*Sinh(4) = Cosh(4)

This is a matter of simplifying how the input of a function is treated.

#### Re: Function...with use of the real, imaginary, and complex values

You are still just describing how Graph works, so I am trying to guess what it is you want. If you for example want to plot a function with the real part on the x-axis and the imaginary part on y-axis then you can use a parametric function like this:

``````x(t) = re(e^[t+t*i])
y(t) = im(e^[t+t*i])``````

#### Re: Function...with use of the real, imaginary, and complex values

Well, if anything I guess I will only learn how to plot two separate functions. I'm starting to think that would be easier on your part if you dealt with more real more urgent requests for Graph. I thank you for taking out your time to consider my requests sir, and if you ever need me, I'm here to help...at least math wise.