Abstract
This chapter discusses complex numbers. Adding and multiplying real and imaginary numbers without restrictions, they formed new numbers a + bi, which are called complex numbers. Complex numbers were used, just as other kinds of numbers without strict verification of laws governing these numbers. The beginning of the 19th century removed all controversies that had arisen round the notion of complex numbers. The first justification given by Gauss showed that complex numbers are really points of the Euclidean plane, where certain operations called addition and multiplication of points were introduced. Another justification, because of Hamilton, introduces complex numbers as pairs of real numbers, defining multiplication and addition of pairs. Both justifications are equivalent, for a point of the Euclidean plane is defined by its pair of coordinates, that is, by a pair of real numbers.
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