If Ziran colossal pushes to activate this power and loses it does it still resolve next turn ?

Yes. The game effect doesn't have a duration, so it isn't an effect that goes away when the text is lost. (I am 85% sure I am correct in this.)

Actually I think it's NO. The power clearly states that it only works if Ziran hasn't taken damage since your last turn. If you use Colossal Stamina or choose to take pushing damage to activate the effect, Ziran will have taken damage since your last turn.

I'm 50% sure I am correct in this.

Your timing is off. The way it goes is:
1: use colossal stamina to give Ziran a power action to use this power
2: take the 1 unavoidable damage from CS
3: end your turn
4: opponent takes turn, and fails to damage Ziran.
5: begin your turn, check for damage since end of last turn.

Note that checking for damage since last turn in step 5, it would only check for damage during step 4. Since your last turn does not include your last turn, the damage from CS would not count against it.

I am i% sure of this, where i equals the square root of -1.

Looks correct.
That's not a real number, is it?

In this case, I don't mind being wrong. It makes him way more awesome.

It is certainly not a real number. It's an imaginary number. Completely different number system.

When did this become a math lecture? Isn't there another forum for that ?

So here's another question if this power were outwitted would it still activate next turn or does countering it stop it?

See post #2.

Getting hit with a planet would hurt. I'm only 22% sure of that.

GAH! NO! People!

Imaginary numbers are real. The term "imaginary" was a derogatory name stuck to them by early mathematicians who didn't understand what they were. But just because they aren't countable, doesn't mean they aren't real. You can't have -1 apples, but negative numbers are real, right? That you can't do some kinds of real world stuff with them doesn't mean they aren't real. Imaginary numbers are important. You can't calculate the orbitals of electrons in atoms without them. You can't do electromagnetic equations without them. Atoms and electromagnetism are real, people!

Imaginary numbers: You can't imagine life without them.

***

You should count yourself lucky if I decide to give you a math lecture! For free! Math is pure and good! And a great deal of fun!

Isn't "real numbers" the term for numbers that are not "imaginary numbers?"

Yes, but, again, it was a derogatory term applied before what they were was understood. It's amazing how often derogatory terminology sticks. "Big Bang" was invented to make fun of the theory, but nobody thinks of it with any other name now.

I think of it as the Horrendous Space Kablooie.

Everyone should.