Showing custom complex data class

I'm just learning about data and I'm trying to somewhat define complex numbers with it.

So far I have the following:

data Complex = Complex Int Int deriving(Eq)

instance Show Complex where
    show Complex a = a -- Not working

instance Num Complex where
    Complex a b + Complex c d = Complex (a+c) (b+d)
    -- etc.

What I'm trying to do is to instance Show in order to make the program print a string like a complex number, such as: "a + bi"

I understand why the code I wrote errors, since a is of type Complex and the program expects a string, but I can't wrap my head around how I can separate both numbers and then add "i" to b, as well as put the operator inbetween.

Any ideas?

Solution

The line

show Complex a = a

defines a function show with two arguments, the first one being Complex and the second one being a. This copes with the signature of show in class Show, where we only find one argument.

Since that argument must be a Complex, you probably want something like

show (Complex a b) = show a ++ " + " ++ show b ++ "i"

Note how we use show on a and b of type Int to convert them to strings, and then concatenate a bunch of strings using ++.

Also note that when b is negative the output of the above is suboptimal. You might want to change the function accordingly.