Complex Analysis: Theory and Applications · Problem 6.6.1

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · fundamental-theorem-of-algebra-liouville

Problem

Factor each polynomial as a product of linear factors. ((a))

P(z) = z^4 + 4

. ((b))

P(z) = z^2 + (1+i)z + 5i

. ((c))

P(z) = z^4 - 4z^3 + 6z^2 - 4z + 5

. ((d))

P(z) = z^3 - (3+3i)z^2 + (-1+6i)z + 3 - i

. Hint: Show that

P(i) = 0