Assignment:
Prove that if p is a polynomial with real coefficients, and if z Ξ [z1 ,z2,...] is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part of z, and the imaginary part of z are also solutions.
Note: This is from a numerical analysis course, and here P(E) refers to a polynomial in E, the “shift operator” for a sequence.
Provide complete and step by step solution for the question and show calculations and use formulas.