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introduction to Complex Numbers
The complex numbers
Are the real numbers not sufficient?
A complex number
A representation of a complex number
Equal complex numbers
Sum of complex numbers
Product of complex numbers
A special product of complex numbers
Notation, sum and product
Opposite complex numbers
Subtraction
Conjugate complex numbers
Modulus of a complex number
The structure C, + , .
Multiplication in practice
Division in practice
Square roots and complex numbers
Square roots of a positive real number
Square roots of strict negative real number
Square roots of a complex number a + ib that is not real
Polar representation of complex numbers
modulus and argument of a complex number
Polar form of complex numbers
Equal numbers in polar representation
Product in polar representation
Conjugate numbers in polar representation
The inverse of a complex number in polar representation
Quotient two complex number in polar representation
Natural power of a complex number
Formula 'De Moivre'
Negative power of a complex number
Other properties of complex numbers
n-th root of a complex number
Polynomials and complex numbers
Properties
Theorem of d'Alembert
Number of roots of a polynomial equation
Roots of a polynomial equation with real coefficients.
Factorization of a polynomial with real coefficients
Sum and product of the roots of a polynomial equation
JEE Zone
(2007)