I dint understand A SINGLE THING in the latest maths lecture. he started with theroem 1: I am just going to type some lines so that someone of you might recognize this as something and can tell me the name of the theory coz our lecturer just called it "theorem 1" (wth!!!!!!) I searched the internet for 2 hours and couldnt find anything; anyway here goes:

if p(z) = a0 + a1 z + a2 z + .........

where a0,1,2,3,n are real numbers and z may be complex then this polynomial has a solution w, which is complex such that p(w)=0.

Moreover, if the root w has non zero imaginary part and y is the conjugate of w then p(y)=0.

If p(w)=0

then we can write p(z)=(z-w)q(z)

*WHY??????????????? our lecturer just assumed that!!! anyway then he wrote:*

where q is another polynomial. Moreover the degree of p is n and the degree of q is n-1 Now we can apply Theorem1 to q and find u so that q(u)=0 and so q(z)=(z-u) r(z)

Hence

p(z)=(z-w) (z-u) r(z)

and continuing in the same amnner we can completely factorize

p(z) in products of linear factors.

thank you very much for helping in advance.