Original Lyrics Imagine there's no Heaven It's easy if you try No hell below us Above us only sky Imagine all the people Living for today ah-aaa- Imagine there's no countries It isn't hard to do Nothing to kill or die for And no religion too Imagine all the people Living life in peace You may say that I'm a dreamer But I'm not the only one I hope someday you'll join us And the world will be as one Imagine no possessions I wonder if you can No need for greed or hunger A brotherhood of man Imagine all the people Sharing all the world You may say that I'm a dreamer But I'm not the only one I hope someday you'll join us And the world will live as one | Imagine there's a number More complex than pi You can't resolve its value Not even if you try Imagine there's a number square root of minus one i-i-iii Imaginary numbers So many things they do They're used in maths and physics and engineering too Imaginary Numbers Imagine one today! ooooo You may say "I love Euler!" For e to the i pi plus one Brings us back down to zero And is as perfect as they come Imaginary numbers may bamboozle you but it can make things simpler sine and cosine too Imaginary numbers set your mind at peace You may say I am Riemann With a root of minus one I hope some day we can solve it And we'll have a continuum Alternative verses: 2nd verse: Imagine there's no answer it isn't hard to do no zeros to solve for no graphing too imagine all these problems solved with i in place. 3rd verse: Imagine all the functions That you've had to shun see i can make them simpler like Euler's rule has done Imaginary numbers Bring you QED Chorus: You may say that we're crazy There's no square root minus one But I assure you we all love them\I hope some day you will get them it's as perfect as they come |