Finding Kernel of P: Steps to Show Ker(P) is in Ker(P°P)

[Maths2468]

I have a linear transformation P:z→z
I want to show the Kernel (p) is a subset of the kernel (P ° P)

I know that the composite function is defined by (P ° P)(x)=P(P(x))

Where do I begin with this?
To find ker(P) I would do P(x)=0 but I am not sure how I would do this here.

What steps should I follow?

 

[Mandelbroth]

I have a linear transformation P:z→z
I want to show the Kernel (p) is a subset of the kernel (P ° P)

I know that the composite function is defined by (P ° P)(x)=P(P(x))

Where do I begin with this?
To find ker(P) I would do P(x)=0 but I am not sure how I would do this here.

What steps should I follow?

We want to find elements $x$ such that $P(x)\in\operatorname{ker}(P)$. Is 0 such an element?