No, a zygote isn't a person because I conceive the zygote to be a person. A zygote is a person because of biological continuity of the individual from conception onwards.
This is a key assumption in child support - that this continuity exists. No continuity = no child support payments.
Continuity is bad argument. More zygotes get lost in periods than become humans. All humans die, how about that for biological continuity. We have to take matters into account for what they are now, not for what they may be later.
If zygotes are people do they count in censuses? Do they get social security numbers? Do natural terminations count as causes of death? If so, step aside cancer or heart disease or any other diseases, because far and away more zygotes "die" than any other cause of death. If a zygote is a person does that mean identical twins are the same person? Are genetic chimeras two people?
Conception is a process, so life at conception is a meaningless phrase and I have yet to meet a single "pro-life" person who is intellectually honest about the implications of their supposed belief.
If a person is "pro-life", if they think that the bundle of cells that sometimes can't be seen by the human eye is a human, they should agree with Trump - either the mother is commitng murder or hiring a hitman.