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The Complex Domain

Problem :compute the rectangular form a+ib of .

>> rectform(ln(3+4*I));

                            ln(5) + I atan(4/3)

The real and imaginary part are obtained with Re(..) and Im(..) respectively.

[New] Problem :compute the rectangular form of .

>> rectform(tan(x+I*y),{x,y});

                      sin(2 x)             I sinh(2 y)     
                -------------------- + --------------------
                cos(2 x) + cosh(2 y)   cos(2 x) + cosh(2 y)

Here the set {x,y} given as second argument specifies that the variables x and y are real. By default all variables are considered as complex.

Problem :do not simplify to 0 without any assumption on the imaginary part of z.

>> sqrt(exp(z))-exp(z/2);

                                / z \         1/2
                          - exp | - | + exp(z)   
                                \ 2 /

Andre Heck
Sun Apr 23 10:32:10 MDT 1995