I am programming a numerical application and I managed to get rid of all the sine and cosine usages except for the calculation of the Cartesian form of an array of complex numbers from their polar form.
given a complex number $z_p = \rho ^\theta$, I need to get the Cartesian form $z_c = a + i \cdot b$.
Usually I do:
$$ z_c = \rho \cdot (cos(\theta) + i \cdot sin(\theta)) $$
Which is what I want to avoid because it uses sine and cosine. I also know this other way:
$$ z_c = \rho \cdot e^{- i\theta} $$ But it boils down to using sine and cosine as in the previous formula (see Euler's formula)
is there any other way?