Properties of the Complex Number System :
Properties of the Complex Number System The complex number system contains all real numbers
Addition, subtraction, multiplication, and division of complex numbers obey the same rules of arithmetic that hold in the real number system, with one exception:
the exponent laws hold for integer exponents, but not necessarily for fractional ones
Slide 3:
The complex number system contains a number, denoted i , such that
Every complex number can be written in the standard form a + bi, where a and b are real numbers.
a + bi = c + di iff a = c and b = d.
Square Roots of Negative Numbers :
Square Roots of Negative Numbers Let b be a positive real number.
is defined to be
Conjugate Solutions :
Conjugate Solutions If a + bi is a solution of a polynomial equation with real coefficients, then its conjugate, a – bi, is also a solution of the equation.