let-P-x-1-ix-n-1-ni-with-x-real-and-n-integr-natural-1-find-the-roots-of-P-x-2-factorize-P-x-inside-C-x-3-factorize-P-x-inside-R-x-4-decompose-the-fraction-F-x-P-1-x-P-x-

Question Number 57947 by maxmathsup by imad last updated on 14/Apr/19

l e t P (x) = {(1 + i x)}^{n} - 1 - n i w i t h x r e a l a n d n i n t e g r n a t u r a l

1) f i n d t h e r o o t s o f P (x)

2) f a c t o r i z e P (x) i n s i d e C [x]

3) f a c t o r i z e P (x) i n s i d e R [x]

4) d e c o m p o s e t h e f r a c t i o n F (x) = \frac{P^{(1)} (x)}{P (x)} i n s i d e C (x)

P^{(1)} i s t h e d e r i v a t i v e o f P .