Structure Beyond C

Ask: NZQRC...X?
(Nine Zulu Queens Rule China ...)
Is there a number system X beyond Complex C?

We know that Z is extended of N
because of solving equation like :
y+2=0
=> y= -2 ∈Z

Similarly Q extends Z:
3y-2 =0
=> y= 2/3 ∈ Q

R extends Q:
y² = 2
=> y = √2 ∈ R

C extends R:
y² = -1
=> y = √-1 ∈ C

What about something extends C ?
Answer: No such number system !

Why ?

Let the Polynomial equation
P(x) = xⁿ +...+ dx³+ cx² + bx + a

P(x) has n solutions in C (by Gauss Fundamental Law of Algebra): z0, z1, z2, ...zn-1
P(x) can be factorized as:
P(x) = (x-z0).(x-z1).(x-z2)....(x -zn-1)

P(x)=0 has all n complex solutions still in C
=> closed in C or Complete in C
=> no need to extend C like the previous number systems (NZQR)