Download Complex Variables by George Polya, Gordon Latta PDF

By George Polya, Gordon Latta

Show description

Read or Download Complex Variables PDF

Best nonfiction_4 books

Patent and Trademark Tactics and Practice, 3rd edition

The fundamental highbrow estate reference for all parts of technological know-how and technology--covering patents, emblems, copyrights, and exchange secretsDid you recognize patent doesn't supply its proprietor the suitable to make, use, or promote the discovery coated by way of his patent? trademark want by no means be registered with a view to sue others for infringing on it?

Additional info for Complex Variables

Sample text

20 Describe the region formed by those points z for which the term z"fn ! is greater in absolute value than the other terms of the infinite series z z2 z3 DoZ + 1 +- +- +- + ··· 3! 2! 1! 21 Let A and B denote complex constants, and z a complex variable. ,t: 0, and show that A + A + Bz + Bz = 0 is the equation of an (arbitrary) straight line. 22 Let A, B, and C denote complex constants, and z a complex variable. 4 + Bz + Bz + ( C + C) z1. = 0 is the equation of an (arbitrary) circle. , determine the three vertices of a triangle, and w, wit w2 the corresponding vertices of another triangle.

For instance, they lead quickly to various expressions for 1 /z, the reciprocal of z: Let us write 1 Z X -iy 1 - = -2 = 2 = - (cos 6 - i sin 6 ) z lz1 x + y2 r z1 = x1 + i y1 = r1 (cos 6 1 + i sin 6J where x1 , y 1 0 rh 61 are real and r1 positive, as the notation suggests. Then we can express the quotient z1/z as follows : r1 z1 z1z = 2 = - [cos (6 1 - 6 ) + ism (6 1 - 6 )] r z lzl If we wish to write the conjugate of a composite expression we use longer horizontal lines. For instance, if we suppose, as usual that x and y are real, z2 = (x + iy)2 = x2 - y2 - 2ixy .

If n is an integer. sin 2n7T = 0 cos 2n7T = 1 Consequences of Euler's Theorem 41 and therefore e12 11 " = cos 2mr + ; sin 2mr = 1 (3) Hence (4) This last equation is apparently more general than (2) which is contained i n it as a special case for n = 1 . But we may easily derive (4) from ( 2) by repeated application. For instance, We obtain similarly that and so on. (c) Since cos we have 11' = -1 sin 11' =0 ei" = cos 11' + i sin 11' = - 1 We may remember this result in the form ei " + 1 = 0 (5) Somebody called this the "most beautiful" formula since, he said, it combines the five "most important" numbers, 0, 1 , i, 11', and e.

Download PDF sample

Download Complex Variables by George Polya, Gordon Latta PDF
Rated 4.65 of 5 – based on 48 votes