 For example, if the curve where the real part is known is the real line, then we can add "i" times any self-conjugate function.If the curve forms a loop, then it is determined by the real part of the function on the loop since the only functions whose real part is zero on the curve are those that are everywhere equal to some imaginary number.The Weierstrass factorization theorem asserts that any entire function can be represented by a product involving its zeroes (or "roots").