My safety pilot is endorsed for complex, and will be PIC for the entire flight. I would also log PIC for the time I spend under the hood.
I will eventually get my complex endorsement, but insurance is much cheaper if I have time in type, so in the long run it will be cheaper for me to build time in type and work towards my instrument rating at the same time.
Yes. You can, as long as you have the appropriate rating and are the sole manipulator of controls. From a FAA response to a similar question:
... a private pilot may log pilot-in-command time, in a complex or high performance airplane, for those portions of the flight when he or she is the sole manipulator of the controls because the aircraft being operated is single-engine land and the private pilot holds a single-engine land rating.
... 14 CFR section 61.31 requires a person to have an endorsement from an authorized instructor before he or she may act as pilot in command of certain aircraft (a complex airplane, a high performance airplane, a pressurized airplane capable of operating at high altitudes, or a tailwheel airplane). These endorsements are not required to log pilot-in-command time under 14 CFR section 61.51(e). (emphasis mine)
Excerpt from §61.51 Pilot logbooks:
(e) Logging pilot-in-command flight time.
(1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-
(iv) When the pilot performs the duties of pilot in command while under the supervision of a qualified pilot in command provided—
(A) The pilot performing the duties of pilot in command holds a commercial or airline transport pilot certificate and aircraft rating that is appropriate to the category and class of aircraft being flown, if a class rating is appropriate
Yes.
You can log actual and simulated instrument time while being the sole manipulator of the controls without the complex endorsement.
See FAR 61.51.
