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

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.

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

]]>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]

**$matches[1]**. 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.

]]>