If [math]a^2 + b^2 = 1, c^2 + d^2 = 1,\; a^c + b^d = 0,[/math] then what is the value of [math]ab+cd[/math] if [math]a, b, c,[/math] and [math]d[/math] are not zero and real numbers?
What is the greatest trick in mathematics?