For two days I investigated brother Leo, and when I wasn't investigating him I was questioning him. The small town in Minnesota where he claimed he and his brother were born had been the county seat, and the whole shivaree had burned up in a prairie fire years ago, courthouse, birth records and all. With no other living relatives, I had to depend on people who had known both men. From those whom I questioned, I ascertained that they had been passing for brothers, at least, for some time. On the third day Leo's patience began to crack. "You keep asking me the same, stupid questions over and over. I tell you, I'm a mechanical engineer. My brother was a mathematician. We're both single. I make enough money in the construction game to support both of us. What's so suspicious about humoring my brother's research?" "Among other things," I said, "is your ignorance of what he was doing." "For the fiftieth time I tell you I _didn't_ know!" His exasperation was mounting to the pitch I had been awaiting. "You used the past tense. You do know now?" He wheeled and crossed the living room, poured himself a drink of straight bourbon and downed it. "Yes, I have a notion now, but it's none of your damned business. His ideas may be patentable." I said slowly and quietly, "Now I'll tell you what I've been waiting for. I've been waiting for you to offer me information about the two little gadgets that you removed from your brother's work-bench--against my explicit orders not to touch anything. Until you produce those items and explain your actions I'll be around here asking stupid questions. From now on, understand?" "Damn cops!" He threw the shot glass to the floor and glared at me for a long minute. "All right, come with me." We went into a little library. He took two volumes from a high shelf and from the recess snatched the two gadgets with the pistol grips. From a table drawer, which he unlocked with a key from his pocket, he took some drawings that looked like the ones that had disappeared from his brother's little workshop. "Calvin developed a new effect by applying one of his esoteric mathematical symbols to a simple electronic circuit," Leo began, in his surly tone. He pointed at the margin of the circuit drawing. There were jottings of algebraic formulae in which the quantity "i" appeared prominently. He pointed this out to me and continued, "Being a cop you wouldn't understand, but this symbol stands for an imaginary number, the square root of a minus one." This rang a bell from away back in my own college math. I said, "Yeah, I think I remember. It's some sort of operational factor in polar coordinates. No real meaning in itself, but--" "Well! An educated cop! That's right, except that Calvin managed to give this symbol an actual, functional application. I was telling the truth when I said I didn't know what he was doing. I still don't understand it, and I've been losing sleep over these formulae."