The C128 was a C64 with an extra CPU as well as extra memory. But the second CPU was a Zilog Z80 while the primary was the usual Commodore CPU, a MOS 6502.
The Z80 was there so that CP/M software could be run and as such the machine has a C64 mode using the 6502 and a CP/M mode using the Z80.
But was it possible to write software for it that ran on the Z80 outside of the CP/M environment, and if so did the Z80 have full access to all the machine's custom hardware such as sprites, SID sound chip, etc?
I believe the Z80 had to run slower than usual on this system, so for performance the 6502 would normally be used. But if you still wanted to code for the Z80 rather than the 6502 could you still use all the system's hardware features?