Conjugate, modulus and division by hand

Python can do complex arithmetic for you. Here you write it yourself, with each number kept as two real numbers: $a + ib$ is the pair (a, b).

The idea. $\dfrac{a + ib}{c + id} = \dfrac{(a + ib)(c - id)}{c^2 + d^2}$. Expand the top to find its real and imaginary parts.

Your tasks.

1. In conjugate, return the conjugate of $a + ib$ as a pair.
2. In modulus, return $|a + ib|$.
3. In divide, return $\dfrac{a + ib}{c + id}$ as a pair.