Method and apparatus for determining the exponential powers of "i"
OwnerRuben V. Marceloinventor
Life of this patent
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Abstract
The present invention provides methods and apparatus for readily determining the value of the imaginary number "i" raised to different exponential powers. Calculations pertaining to the imaginary "i" are commonly encountered in engineering, mathematical and scientific calculations and analysis. In accordance with the present invention, the value of "i" raised to any magnitude of exponential power is readily determined based upon the values of the "ones" and "tens" place of the exponent, including whether the "tens" value is an even or odd integer. Different apparatus are provided for readily calculating the value of the imaginary number "i" for any natural number of exponential power.
Claims18
An apparatus for determining the value of the power of the imaginary number "i", said apparatus including a base having a first outer surface carrying at least two aligned scales, one of said scales corresponding to the tens digit of an exponent to which said imaginary number "i" is raised, the other of said scales corresponding to the "ones" digit of said exponent.
An apparatus for determining the power of the imaginary number "i", said apparatus including a sleeve having a first notched portion proximate to one end thereof and an opening defined on at least one outer surface of said sleeve;
- a circular element rotatably mounted within the sleeve, said circular element carrying at least two concentric scales, one of said scales corresponding to the ones digit of said exponent to which said imaginary number "i" is raised, and the other of said scales corresponding to the power of said imaginary "i";
- said power of said imaginary number "i" in said opening corresponding to said ones digit observed in said first notched portion of said sleeve.
An apparatus for determining the power of the imaginary "i", said apparatus including first and second connected elements, said first and second elements being movably mounted relative to each other;
- said first element including a scale corresponding to the tens digit of an exponent to which said imaginary number "i" is raised when said tens digit is odd, said second element including a scale corresponding to the tens digit of an exponent to which said imaginary number "i" is raised when said exponent is even;
- each of said first and second elements including rows of digits corresponding to the ones digit of said exponent;
- and an intermediate element connected to and mounted between said first and second elements, said intermediate member including a scale selectively exposed by moving said first and second elements relatively apart from each other, said scale on said intermediate element corresponding to the power of said imaginary number "i".
Dependencies are inferred from the claim text.