Need Of Complex Numbers

COMPLEX ANALYSIS

Need Of Complex Numbers

Some quadratic equations which have no solutions in real numbers. 
For Example
1.    \fn_cm x^2+4=0
2.   \fn_cm x^2+x+1=0
3.   \fn_cm x^2-2x+3=0
In order to find the solutions of above given or similar quadratic equations, the symbol \fn_cm \fn_cm ” i  ”  was used.  Euler was the first person to introduce the symbol ” i “. where          \fn_cm i=\sqrt{-1}\,\, or \,\,\ i^2=-1
                    Gauss ( 1777-1855) was a German Mathematician and was a first person to prove  in satisfactory manner that there are some algebraic equations which have real coefficients have complex roots in the form of  \fn_cm a \pm i b.
  Note:   complex and irrational roots always occur in pairs.

              

             

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