$\mathbb Z_2=\{e, \xi\}$ when $\xi^2=e$
$\mathbb C\mathbb Z_2=\{ae+b\xi |a, b\in\mathbb C\}$
$f:\mathbb C\mathbb Z_2\rightarrow \mathbb C\bigoplus \mathbb C\ae+b\xi\mapsto (a+b,a-b)$
show that f is a ring isomorphism.
I got all parts but f is onto. I mean I showed f is ring homomorphism and one-to-one, but don't know how to show it is onto.
Please, help

Question

$\mathbb Z_2=\{e, \xi\}$ when $\xi^2=e$
$\mathbb C\mathbb Z_2=\{ae+b\xi |a, b\in\mathbb C\}$
$f:\mathbb C\mathbb Z_2\rightarrow \mathbb C\bigoplus \mathbb C\ae+b\xi\mapsto (a+b,a-b)$
show that f is a ring isomorphism.
I got all parts but f is onto. I mean I showed f is ring homomorphism and one-to-one, but don't know how to show it is onto. 
Please, help

ganeshie8 · Answer

@Zarkon

campbell_st · Answer

Outside my range @ Loser, sorry I can't help

loser66 · Answer

Thanks for replying though :)

dan815 · Answer

i do not understand this question please teach me all the background info i need to know

dan815 · Answer

if u dont teach me ill report you to a mod

dan815 · Answer

im gonna tell them that you msgsed me indecent msgs -.-

dan815 · Answer

bahahahaha

loser66 · Answer

@dan815  but I don't see anything different from normal proof of onto function. Ignore the weird notation, it's just a function, right? and we just prove as usual, right? but how? hahaha