> 
> Given $ a= (x\_1,x\_2), b= (y\_1,y\_2) \in \mathbb{C}^2 $ and $f(a,b) = x\_1\bar y\_2 - \bar x\_2 y\_1$
> 
> 
> Now my question: Is $f$ a bilnear
> form on $\mathbb{C}^2$ ?
> 
> 
> 

My attempt: i know that for a bilinear form, we have $f(ka\_1 +b\_1 , c\_1) = k f(a\_1,c\_1) + f(b\_1, c\_1)$.

But here I don't know how to check whether $f$ is bilnear form or not ?

Any hints/solution will be appreciated