Rectangular form of $z$ without cosine and sine

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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?