RE: unknown complex polynomial

[Martoman]

Find a polynomial equation of the lowest possible degree having roots of 1+2i and -3 if the coefficients are real and complex.

I get the complex one easily, multiply the roots in factored form then you get a polynomial degree 2 with complex coefficients. The real part is annoying me, I've attempted to sub in to the general but that just becomes ewwwy as i need more information for the three unknowns.

[Damo17]

complex conjugates...

[lastq]

If the coefficients are real, then the complex roots occur in conjugate pairs. ie if 1+2i is a root, then so is 1-2i.

Hence p(z) = (z-1-2i)(z-1+2i)(z+3)
= (z^2-2z+5)(z+3)
= z^3+z^2-z+15

Therefore the equation is z^3+z^2-z+15=0

[Martoman]

arg.. fuck... thanks guys. Here is a good example of NOT reading the question. Here I was confounded by the fact that we couldn't possibly have only 2 solutions if its real and the highest power was z^2.... maybe i should listen to my intuition more... or learn to read English.