LOGARITHMS OF IMAGINARY NUMBERS IN RECTANGULAR FORM: A NEW TECHNIQUE Page No: 3131-3137

Ashwani K Thukral

Keywords: Rectangular and polar form logarithms, Euler’s equation, imaginary exponential function, logarithmic multiplication and division of imaginary numbers, computational sciences

Abstract: Logarithms of imaginary numbers are defined by Euler’s equation in polar form with real X-axis and imaginary Y-axis. In the present paper, a new concept of logarithms is developed from the basic principles to derive the logarithms of imaginary numbers in rectangular form with both X and Y axes being imaginary. Logarithms of imaginary numbers to a real base with an imaginary multiplicative coefficient are real numbers. This concept generalizes the multiplication and division of real and imaginary numbers using logarithms in rectangular form.



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