I have expressed a complex polynomial in terms of its six linear factors, as $(z - x_0)(z - x_1)$ etc., where each x is a root in exponential polar form.
I have been able to express one conjugate pair of factors instead using cartesian form for the root. I can then multiply out that pair of factors and express the result in a simpler form.
The other pairs however I do not know how to express in cartesian form, as I am unable to determine the real and imaginary values from the exponential form.
Is there a formula/shortcut/simpler way of multiplying out linear factors corresponding to conjugate pairs of roots while the roots are in exponential form?
Otherwise my result is a large and seemingly messy number of terms that must continue to be multiplied out.