Take the numerator and denominator as a pair of complex numbers.

The modulus of both the numerator and denominator is by Pythagoras' theorem.

The angle of the complex number in the numerator is

The angle of the complex number in the denominator is

Use De Moivre's theorem to calculate the powers, thereby writing both numerator and denominator in polar form.

To divide 2 complex numbers in polar form, you calculate the ratio of their moduli and subtract their angles.

Then with the result evaluated in polar form, you may convert that to Cartesian Form if necessary.