Do exist such entities like functions of hypercomplex variable ?
79637
Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.\n\nThe first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.\n\nThe development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functions of the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.\n\nIn the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.\n\nThe book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.\n\nAudience \nUniversity libraries. Libraries of research institutes for mathematics and physics. Departments of mathematics and physics of universities. Departments of mathematics and theoretical physics of research institutes.
848767
yoiu can do the same by vedic maths as mentioned in the link below
80323
No. xy = k is an hyperbola in 2D. xy = kz is an hyperboloid on 3D.
276224
these guys do it much better than i can:\n\nhttp://hyperphysics.phy-astr.gsu.edu/Hbase/class/phscilab/kundt2.html
654434
Yes, there is. The square root of negative 1 is the number i, which is an "Imaginary Number." \n\nDespite the name, imaginary numbers are real quantities that are used in equations to get real answers. However, they are a somewhat confusing concept, mathematically. \n\nOne way to visualize them is to consider that multiplication by an imaginary number rotates a function orthogonally on a number axis. The answers given by performing this procedure once may not seem to be applicable to real situatons, but if you multiply by an imaginary number again, in rotates the function back onto the initial axis, yielding real number results. \n\nI am including links to a number of good sites on imaginary numbers. Although it can be difficult to understand the implications of imaginary numbers beyond the fact that their squares are negative, if you spend some time on these sites, I'm sure you'll come to understand them.
663777
SOrry, I can't help you. If I had the formulas I could do it, but there is no way I remember that off the top of my head! Good luck
907364
Almost.  You would actually include the endpoints 0 and -3 (so you need to use a bracket instead of parentheses).\nD = [0, infinity)\nR = [-3, infinity)
240384
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
115042
I believe you are talking about Cartesian coordinates, right?
556325
There's a classic one:  "Complex variable" written by Churchill.  It's a very understandable book.\n\nHowever if you're looking for something more advanced, "complex variable" written by Conway it's a good option.\n\nIf you do analysis, you can use another classic: "Real and Complex Analysis" of Rudin.
207605
bool function(int a, int b, int c)\n{\nreturn a || b || c;\n}
246218
Probably something along the lines of it exists in a 3d matrix on an x-axis, y-axis, and z-axis and containing height, depth, and length.
353544
http://mathforum.org/library/drmath/sets/high_calculus.html\n\nask here...:)
547629
assuming u is an unknown variable y=0
182274
...found first counterexample to Dowker's conjecture that normality in topological spaces is preserved under cross product with the closed unit interval of the reals.\n\n...assuming the continuum hypothesis proved that the box topology on the product of countably many copies of the reals is paracompact.
1154622
a variable quantity that can be resolved into components
241658
YES !!!\nA variable y is a function of x if a relation between x and y produces exactly one value of y for each value of x.\n\nThis is not a higher education question !