bellenot 2318> maple
    |\^/|     Maple 8 (SUN SPARC SOLARIS)
._|\|   |/|_. Copyright (c) 2002 by Waterloo Maple Inc.
 \  MAPLE  /  All rights reserved. Maple is a registered trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> simplify((1+2*I)/(3-4*I)+(2-I)/(5*I));
                                     -2/5

> simplify(5*I/((1-I)*(2-I)*(3-I)));
                                     -1/2

> simplify((1-I)^4);
                                      -4

> Z:=I/(-2-2*I):arctan(Im(Z),Re(Z));
                                      3 Pi
                                    - ----
                                       4

> Z:=(sqrt(3)-I)^6:arctan(Im(Z),Re(Z));
                                        1/2     6
                                   Im((3    - I) )
                            arctan(---------------)
                                        1/2     6
                                   Re((3    - I) )

> Z:=expand((sqrt(3)-I)^6):arctan(Im(Z),Re(Z));
                                      Pi

> solve(a*x^3+b*x^2+c*x+d=0,x);
  1/3               2
%1      2 (3 c a - b )    b
----- - -------------- - ---,
 6 a            1/3      3 a
          3 a %1

        1/3            2                    /  1/3               2 \
      %1      3 c a - b     b           1/2 |%1      2 (3 c a - b )|
    - ----- + ---------- - --- + 1/2 I 3    |----- + --------------|,
      12 a          1/3    3 a              | 6 a            1/3   |
              3 a %1                        \          3 a %1      /

        1/3            2                    /  1/3               2 \
      %1      3 c a - b     b           1/2 |%1      2 (3 c a - b )|
    - ----- + ---------- - --- - 1/2 I 3    |----- + --------------|
      12 a          1/3    3 a              | 6 a            1/3   |
              3 a %1                        \          3 a %1      /

                        2      3
%1 := 36 c b a - 108 d a  - 8 b

           1/2     3      2  2                    2  2        3 1/2
     + 12 3    (4 c  a - c  b  - 18 c b a d + 27 d  a  + 4 d b )    a