$1,000,000 problem :: Riemann :: Imaginary numbers  
         
     

Can you find a number such that when you square your number, the answer is -1?

Sounds impossible…negative times negative equals positive is what we learn at school.

No ordinary number can be squared to get to -1. But imagine there might be a new number that we hadn't discovered before that could answer this problem. Is this creation or discovery…

It took the revolutionary years in France for people finally to accept the idea of a new number, called an imaginary number and denoted by the symbol i.

Once we have one imaginary number, mathematicians built many more by taking combinations of ordinary numbers with this imaginary number. For example, 5+6i is another imaginary number. It is possible to do arithmetic with these numbers, i.e. add, multiply, divide, even raise numbers to the power of imaginary numbers.

Imaginary numbers were finally accepted after Gauss produced a picture of these numbers
 
2.2.1.1 Arithmetic of imaginary numbers >
 
  Advanced sections
  2.2.1.1 Arithmetic of imaginary numbers
  2.2.1.2 What is sine and cosine
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