Complex.lua

Complex = {}

--constructors
function Complex.new(re, im)
    assert(type(re) == 'number' and type(im) == 'number', "Both arguments passed to Complex.new must be numbers")
    return setmetatable({re = re, im = im}, Complex)
end

function Complex.polar(r, theta)
    assert(type(r) == 'number' and type(theta) == 'number', "Both arguments passed to Complex.new must be numbers")
    return Complex.new(r*math.cos(theta), r*math.sin(theta))
end

--metamethods
function Complex.__tostring(tbl)
    if tbl.re == 0 then
        return tostring(tbl.im) .. "i"
    end
    if tbl.im < 0 then
        return tostring(tbl.re) .. "-" .. tostring(-tbl.im) .. "i"
    else
        return tostring(tbl.re) .. "+" .. tostring(tbl.im) .. "i"
    end
end

function Complex.__unm(tbl)
    return Complex.new(-tbl.re, -tbl.im)
end

function Complex.__add(tbl1, tbl2)
    if getmetatable(tbl1) == Complex then
        if getmetatable(tbl2) == Complex then
            return Complex.new(tbl1.re + tbl2.re, tbl1.im + tbl2.im)
        elseif type(tbl2) == 'number' then
            return Complex.new(tbl1.re + tbl2, tbl1.im)
        else
            error("Attempt to combine a Complex with an invalid type")
        end
    else
        if type(tbl1) == 'number' then
            return Complex.new(tbl1 + tbl2.re, tbl2.im)
        else
            error("Attempt to combine a Complex with an invalid type")
        end
    end
end

function Complex.__sub(tbl1, tbl2)
    return tbl1 + (-tbl2)
end

function Complex.__mul(tbl1, tbl2)
    if getmetatable(tbl1) == Complex then
        if getmetatable(tbl2) == Complex then
            return Complex.new(tbl1.re*tbl2.re - tbl1.im*tbl2.im, tbl1.re*tbl2.im + tbl2.re*tbl1.im)
        elseif type(tbl2) == 'number' then
            return Complex.new(tbl1.re * tbl2, tbl1.im * tbl2)
        else
            error("Attempt to combine a Complex with an invalid type")
        end
    else
        if type(tbl1) == 'number' then
            return Complex.new(tbl1 * tbl2.re, tbl1 * tbl2.im)
        else
            error("Attempt to combine a Complex with an invalid type")
        end
    end
end

function Complex.__div(tbl1, tbl2)
    if getmetatable(tbl1) == Complex then
        if getmetatable(tbl2) == Complex then
            return (tbl1 * tbl2:conj()) / tbl2:times_conj()
        elseif type(tbl2) == 'number' then
            return Complex.new(tbl1.re / tbl2, tbl1.im / tbl2)
        else
            error("Attempt to combine a Complex with an invalid type")
        end
    else
        if type(tbl1) == 'number' then
            return (tbl1 / tbl2:times_conj()) * tbl2:conj()
        else
            error("Attempt to combine a Complex with an invalid type")
        end
    end
end

function Complex.__pow(tbl1, tbl2)
    --do later
end

function Complex.__eq(tbl1, tbl2)
    return tbl1.re == tbl2.re and tbl1.im == tbl2.im
end

Complex.__index = Complex

--methods
function Complex.conj(self)
    return Complex.new(self.re, -self.im)
end

function Complex.times_conj(self)
    return self.re ^ 2 + self.im ^ 2
end

function Complex.to_polar(self)
    return (self.re^2 + self.im^2)^.5, math.atan2(self.re, self.im)
end