The Hunt for i

Look here, boy. I've seen and done more things than you can ever imagine. I've travelled past the wall of Quadratics into the wilderness of Polynomials, where I've seen higher degrees than you could ever count.
I've charted graphs with turning points the size of an elephant, and asymptotes to match.
I've wrestled with surds, battled over indices, and expanded more brackets than you could shake a stick at.
Yet for 20 years now, I have been gripped by the most elusive prey of all - i.

I first heard of this tricky beast in a bar in the Domain of the Real, chatting to a pretty little irrational, when silence fell, and a -1 walked through the doors. As we all stared at this outsider in our midst, a Pi near the door stood up and grabbed it roughly from behind.

"Sorry boy. Irrationals only in this part of town."

But -1 just winked, and then did something I thought impossible - rooted itself. The room was in chaos, and I was sprinting towards the site, but arrived too late. I looked at the window to see i disappearing round the corner.

After that, the chase was on. Hopping onto my faithful Axiom, I followed its tracks as fast as I could, but the trail was getting cold fast. It petered out eventually when I was in Trigonometry Town.

I asked a nearby Cosine if it had seen any imaginary numbers nearby, and it looked shifty and muttered something, walking quickly away. My hackles were raised and my guard was down. I had always thought there was something fishy about these periodic functions, and it seems I was justified - they were in cahoots with i.

Walking past some women catching a Tan in the midday sun, I spotted it! i jumped onto the back of a Sin(Pi/2) and was gone in a flash. I ran to the cliff where they were last, but could only see Exponential Territory - yet there was no apparent route to get there from Trigonometry Town. What was the link?!?

I heard a snuffling down by feet, and saw a baby Cosh, begging for scraps. I nudged it with my foot, to give me some space to think, and idly watched it walk away over the cliff, and vanished. I stood, dumbfounded, when I saw the path, infinite yet almost invisible - Maclaurin Series!

Differentiating f(0) with every step, I arrived in Exponential Territory, only to be disgusted with what I saw. Innocent integers were everywhere, scuttling underfoot of the omnipotent e. The numbers were clearly slaves to their irrational masters, who walked away with their indexes bare for all the world to see. I turned a corner, and stopped in amazement. There was one of my dearest friends, Pi, cavorting with both e and i, my enemies. They stopped when they saw me watching, and before I could blink, equalised into -1, which quickly differentiated and was gone.

I have never given up my search, but have had no luck. Nowhere in the Domain of the Real can I find this elusive number i, and much darkness has been uncovered by my searching. Yet I feel sure that the truth is out there, somewhere. Perhaps one day we shall leave this Number Line and advance into the Complex Space, to find a new world that we have scarcely dreamed of.

If there is such a number as i, and it has not been some imaginary dream, that is where it will be found.