Question 12, c d e ,please
11. Differentiate e" sin(a) + ie cos(x). 12. If z=a a ib. , where a and b are real, then the conjugate, is given by Let z = a + ib and w = c + id be any complex numbers. a) Verify that z + w b) Verify that . for any splain why the previous part of this exercise means that positive integer k. P(E) P) then Zo is also a root. (Hint- If 2o is a root of P(z) then what must the d) LetP(z) +Pnz" with po, pi, , pn real. Show that ä¸Po + p12 + e) Show that if 20 is a root of the polynomial P(z) from the previous part, value of P(z0) be?) 13. Let P(z) = Po +Piz + +pn;" with po, pi, . , . , pn real. If w is a real number show that P(iu) = P (w) + iwPg(w) where Pl and Pa are polynomials with real coefficients that depend only on w2. (Hint - Split up the even and odd powers