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In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued. The simplest case arises in taking the square root of a positive real number. For example, 4 has two square roots: 2 and –2; of these the positive root, 2, is considered the principal root and is denoted as ==Motivation== Consider the complex logarithm function log ''z''. It is defined as the complex number ''w'' such that : Now, for example, say we wish to find log i. This means we want to solve : for ''w''. Clearly iπ/2 is a solution. But is it the only solution? Of course, there are other solutions, which is evidenced by considering the position of i in the complex plane and in particular its argument arg ''i''. We can rotate counterclockwise π/2 radians from 1 to reach i initially, but if we rotate further another 2π we reach i again. So, we can conclude that i(π/2 + 2π) is ''also'' a solution for log i. It becomes clear that we can add any multiple of 2πi to our initial solution to obtain all values for log i. But this has a consequence that may be surprising in comparison of real valued functions: log i does not have one definite value! For log ''z'', we have : for an integer ''k'', where Arg ''z'' is the (principal) argument of ''z'' defined to lie in the interval . Each value of ''k'' determines what is known as a ''branch'' (or ''sheet''), a single-valued component of the multiple-valued log function. The branch corresponding to ''k''=0 is known as the ''principal branch'', and along this branch, the values the function takes are known as the ''principal values''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Principal value」の詳細全文を読む スポンサード リンク
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