Question

Please help with this proof. Thank you

Problem 3 Prove that a polynomial anz" + an-121-1 +...+ajz+ao is a continuous function on the entire complex plane.

Answer 1

page-1 P920blem. 3 N- Let +(2) = anzi tan- t...da, ze ao be a Polynomial of degree in with compeen variable arbitrary, Let zo be any point from the entire complex plane c. we know that a function w=f(2) defined in a set s is said to be continuous at a point ats if limit f(2)=f(a) Za le, if limit f12) exists and eanals 27a the value that of 412) for 7=a. Now limit f2) = limit (anza+an. 2.... 9, 2+0) 2 Zo 2 + 20 - ant & anizot. anpa, zota = f (20) so +22 is continuous at zo, since to be any arbitrary point from entire complen Plane &. Hence t2) z anze any teanga at as is continuous function on the entire compeen Plane. THANK Youl