zsh kill Ctrl + Backspace, Ctrl + Delete

I'll focus on Ctrl+Delete first.

The zsh command to delete a whole word forwards is called kill-word. By default it is bound to Alt+D.

How to make Ctrl+Delete do it too depends on which terminal emulator you are using.

On my system, this works in xterm and Gnome Terminal:

bindkey -M emacs '^[[3;5~' kill-word

and for urxvt, you should do:

bindkey -M emacs '^[[3^' kill-word

If that doesn't work, try typing Ctrl+V Ctrl+Delete to see what the value is on your system.

You could even add both of those together to your .zshrc, or use the output of tput kDC5 instead of hard-coding the sequence.

Ctrl+Backspace seems harder.

On my system, pressing that is the same as pressing just Backspace.

If yours is the same, I think your best option is to use Alt+Backspace or Ctrl+W instead.

On urxvt, for the deleting backwards part, I simply have in my .zshrc the following:

bindkey '^H' backward-kill-word

and it allows me to delete the previous word with ctrl+backspace

Add the following to your ~/.zshrc

bindkey '^H' backward-kill-word
bindkey '5~' kill-word