December 2020
Intermediate to advanced
1064 pages
49h 43m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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17.1 Complex Numbers
INTRODUCTION
You have undoubtedly encountered complex numbers in your earlier courses in mathematics. When you first learned to solve a quadratic equation ax2 + bx + c = 0 by the quadratic formula, you saw that the roots of the equation are not real, that is, complex, whenever the discriminant b2 − 4ac is negative. So, for example, simple equations such as x2 + 5 = 0 and x2 + x + 1 = 0 have no real solutions. For example, the roots of the last equation are 
and 
. If it is assumed that , then the roots are written and .