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2. cis (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Cis_(mathematics)

   x is the argument of the complex number (angle between line to point and x-axis in polar form). The notation is less commonly used in mathematics than Euler's formula , e ix , which offers an even shorter notation for cos x + i sin x , but cis(x) is widely used as a name for this function in software libraries .

3. Difference of two squares - Wikipedia

   en.wikipedia.org/wiki/Difference_of_two_squares

   Galileo's law of odd numbers. A ramification of the difference of consecutive squares, Galileo's law of odd numbers states that the distance covered by an object falling without resistance in uniform gravity in successive equal time intervals is linearly proportional to the odd numbers. That is, if a body falling from rest covers a certain ...

4. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   If K is the field of complex numbers, the fundamental theorem of algebra implies that all p i have degree one, and all numerators are constants. When K is the field of real numbers , some of the p i may be quadratic, so, in the partial fraction decomposition, quotients of linear polynomials by powers of quadratic polynomials may also occur.

5. Complex number - Wikipedia

   en.wikipedia.org/wiki/Complex_number

   A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.

6. Split-complex number - Wikipedia

   en.wikipedia.org/wiki/Split-complex_number

   A split-complex number is an ordered pair of real numbers, written in the form = + where x and y are real numbers and the hyperbolic unit [1] j satisfies = + In the field of complex numbers the imaginary unit i satisfies =

7. Residue (complex analysis) - Wikipedia

   en.wikipedia.org/wiki/Residue_(complex_analysis)

   For a meromorphic function, with a finite set of singularities within a positively oriented simple closed curve which does not pass through any singularity, the value of the contour integral is given according to residue theorem, as: = = ⁡ (,) ⁡ (,). where ⁡ (,), the winding number, is if is in the interior of and if not, simplifying to ...