Transcription of COMPLEX NUMBERS - Stewart Calculus
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COMPLEX NUMBERS - Stewart Calculus
COMPLEX NUMBERSA COMPLEX numbercan be represented by an expression of the form , where andare real NUMBERS and is a symbol with the property that . The COMPLEX num-ber can also be represented by the ordered pair and plotted as a point in aplane (called the Argand plane) as in Figure 1. Thus, the COMPLEX number isidentified with the point .The real partof the COMPLEX number is the real number and the imaginarypartis the real number . Thus, the real part of is and the imaginary part is .Two COMPLEX NUMBERS and are equalif and , that is, their realparts are equal and their imaginary parts are equal. In the Argand plane the horizontal axisis called the real axis and the vertical axis is called the imaginary sum and difference of two COMPLEX NUMBERS are defined by adding or subtractingtheir real parts and their imaginary parts:For instance,The product of COMPLEX NUMBERS is defined so that the usual commutative and distributivelaws hold:Si
COMPLEX NUMBERS A complex numbercan be represented by an expression of the form , where and are real numbers and is a symbol with the property that . The complex num-ber can also be represented by the ordered pair and plotted as a point in a
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