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complex-numbersmodulusmapleexpansion

Expand an expression in Maple contening modulus

I want to develop an expression such as |a+b+c|^2 . I tried the command " expand " but it does not work. ( it works without the modulus )

Solution

  • The issue is that expand is unable to recognize whether a, b and c are positive or negative. So, you make that clear then expand will work the way it should.

    restart:
A:=abs(a+b+c)^2;
assume(a>0,b>0,c>0):expand(A);

    a^2+2*a*b+2*a*c+b^2+2*b*c+c^2

    if

    assume(a>0,b>0,c<0):

    then use

    expand(simplify(A))

    Now, lets take three complex numbers and then take its modulus square,

    B:=abs((a1+b1*I)+(a2+b2*I)+(a3+b3*I))^2;

    Once again the same issue as above. 

    assume(a1>0,b1<0,a2>0,b2<0,a3<0,b3>0):expand(simplify(B));

    a1^2+2*a1*a2+2*a1*a3+a2^2+2*a2*a3+a3^2+b1^2+2*b1*b2+2*b1*b3+b2^2+2*b2*b3+b3^2

    Finally, assign some random values for a's and b's and find modulus,

    subs(a1=1,a2=1,a3=1,b1=1,b2=2,b3=3,B);