Manipulating Complex numbers C#

[werto165]

I'm only taking about a simple console application here. I was just wondering how I would convert :

                                      (once converted)

i^2 + 3i^3  + 4i^4 + 2i^5  ----------------->  -1 - 3i +4 +2i => 3-i

 

So I want to enter any arbitrary number eg i^8 +i^20. So would I have to read as a string and then replace with data from a array or something I'm really confused to what a good solution for this would be. 

 

Something somewhat similar to what google does: 

 

[MrSuperb]

i^x

 

if x%4==0 => i^x == 1

elseif x%2==0 => i^x == -1

else

   y=x-1

   if y%4==0 => i^x == i

   else y%2==0 => i^x == -i

[werto165]

i^x

 

if x%4==0 => i^x == 1

elseif x%2==0 => i^x == -1

else

   y=x-1

   if y%4==0 => i^x == i

   else y%2==0 => i^x == -i

Is there some way to find all the complex numbers within a string I enter though? that's the part I'm really struggling with, I just fucking suck at programming  Eg. if the program finds an i it will continue until it reads the rest of the complex number eg. i^50. Then that could be checked in your pseudo code and then  be changed accordingly changed with like string replacement. 

[MrSuperb]

Is there some way to find all the complex numbers within a string I enter though? that's the part I'm really struggling with, I just fucking suck at programming

 

well ... you could just write yourself a parser ...

[werto165]

well ... you could just write yourself a parser ...

Err, I don't know what that is... Do you have a good links to a tutorial on how to make one? 

[Guest]

Err, I don't know what that is... Do you have a good links to a tutorial on how to make one? 

 

Basically, you walk the input string and identify what each part is and possibly store it in a data structure that makes it easy to find and retrieve those parts.