In the case of a complex function, the complex conjugate is used to accomplish that purpose. When a real positive definite quantity is needed from a real function, the square of the function can be used. This operation has practical utility for the rationalization of complex numbers and the square root of the number times its conjugate is the magnitude of the complex number when expressed in polar form. The utility of the conjugate is that any complex number multiplied by its complex conjugate is a real number: The conjugate of a complex number is that number with the sign of the imaginary part reversed Calculation for multiplication and division The denominator can be forced to be real by multiplying both numerator and denominator by the conjugate of the denominator.Įxpanding puts the result of the division in cartesian form again. Presents difficulties because of the imaginary part of the denominator. The division of complex numbers which are expressed in cartesian form is facilitated by a process called rationalization. The multiplication of complex numbers in cartesian form is binomial multiplicationĭivision is a bit more involved in cartesian form and requires the process called rationalization of the complex number. Complex Numbers Multiplication and Division
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