This type of exercise can be solved using the function : complex_number
A complex number is an ordered pair of two real numbers (a, b).
The conjugate of a complex number `a+i*b` , where a and b are reals, is the complex number `a-i*b`.
The modulus of a complex number z=a+ib (where a and b are real) is the positive real number, denoted |z| , defined by : `|z|=sqrt(a^2+b^2)`.
The plan has a direct orthogonal reference `(O,vec(i),vec(j))`. Lets z a non zero complex number and M its image. Called the amplitude of the complex number z, any measure, expressed in radians, of the angle `(vec(i),vec(OM))`.
A complex number z of argument `theta` and modulus r, can be written in its trigonometric form `z=r(cos(theta)+i*sin(theta))`, |z| = r, arg(z) = `theta`.
For any real `theta`, we note `e^(i*theta)` the complex number `cos(theta)+i*sin(theta)`.
A complex number z of amplitude `theta` and modulus r, can be written in its exponential form `z=r*e^(i*theta)`, |z| = r, arg(z) = `theta`.