So I'm not sure if I am posting in the right section, but here is my question.
Code:
P(X)=(8e^2i)-(2e^4i)(X^2)+3X^3
and |P(0)|=8.
Determine R andθ such that the complex number w=Re^(iθ) satisfies Code:
8e^(2i)-2e^(4i)(w^2)=0
and verify |P(w)|>8.
I have done similar questions to this but never P(X) starting with imaginary numbers.
I know we are making a contradiction to prove that P(0)=8 is the minimum. And we have to find R and theta to do this, but Im not sure where to start.
Heres what I was thinking.
we need to work around x=0 and w=Re^(iθ) [given]
So Code:
P(W)=(8e^2i)-(2e^4i)(w^2)+3w^3
Subbing in Reiθ for W...
P(w)<=|8e2i-2e4i(Reiθ)^2|+3R^3..
not sure if this is right or what do do for here, no Idea how to find this R or θ.
Thanks for the help.