Re: a question about complex variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg21672] Re: [mg21620] a question about complex variable*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Fri, 21 Jan 2000 04:00:30 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

First of all the answer you say you want to get is not always true. The correct answer depends on the values of A and P. Take the simple case A = 3Pi/4 and P=Pi. Then your c will become I, its argument Pi/2 and absolute value 1. On the other hand -2(P+Pi/4) is -10Pi/4 and Tan[A] is -1. Mathematica however, can give you correct answers: In[1]:= c = (-I* Cos[2 P] - Sin[2 P]) Tan[A]; In[2]:= argc = FullSimplify[ComplexExpand[Arg[c], TargetFunctions -> {Re, Im}], A \[Element] Reals && P \[Element] Reals] Out[2]= ArcTan[-Sin[2 A] Sin[2 P], -Cos[2 P] Sin[2 A]] In[3]:= absc = FullSimplify[ComplexExpand[Abs[c], TargetFunctions -> {Re, Im}]] Out[3]= 2 Sqrt[Tan[A] ] This is the best you can do without more information about A and P. For example, if you know that Tan[A]>0 you can now use: In[4]:= Simplify[absc, Tan[A] > 0] Out[4]= Tan[A] Again, if, for example, you know that A lies between 0 and Pi/2 (first quarter) you can further get: In[5]:= Simplify[argc, 0 < A < Pi/2] Out[5]= ArcTan[-Sin[2 P], -Cos[2 P]] This means that the argument of c has tangent equal to Cot[2P] and also tells you the quadrant in which it lies. Andrzej Kozlowski Toyama International University JAPAN http://sigma.tuins.ac.jp > From: ZHU Xiaopeng <xpzhu at red.semi.ac.cn> To: mathgroup at smc.vnet.net > Date: Tue, 18 Jan 2000 02:35:10 -0500 (EST) > To: mathgroup at smc.vnet.net > Subject: [mg21672] [mg21620] a question about complex variable > > In my algebra computation, I obtain a expression: > C = (- I Cos[2 P] - Sin[2 P]) Tan[A] > P,A are real variables. Apperently, the argument of C is -2(P+Pi/4) and the > absolute value of C is Tan[A]. But when I use Arg[C] and Abs[C], Mathematica > tells me: > > Out[41]=Abs[(-I Cos[2 P] - Sin[2 P]) Tan[A]] > Out[42]=Arg[(-I Cos[2 P] - Sin[2 P]) Tan[A]] > > This problem appeared at beginning of the computation. I have no idea to deal > with it, so the expressions become longer and longer during the computation. > Can somebody help me? > > >