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complex numbers in Symbolic Toolbox

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Juraj
Juraj 2011년 9월 1일
댓글: Walter Roberson 2017년 11월 3일
Seems, I don't understand the meaning of imag and real in Symbolic Toolbox.
Suppose the following syms a b c d, F=(a+j*b)/(c+j*d). imag(F) gives -1/2*i*((a+i*b)/(c+i*d)-conj((a+i*b)/(c+i*d)))
This is obviously true, but practically for no use; I would like to see the result as
(bc-ad)/(c^2+d^2)
Or, another and simpler example:
F=a+j*b, imF=imag(F) gives -1/2*i*(a+i*b-conj(a+i*b)); The expressions for real(F) or imag(F) may not contain imaginary unit i. The expected answer would be imF=b.
Do you know a solution?
  댓글 수: 1
Walter Roberson
Walter Roberson 2011년 9월 1일
Opps! I deleted some of the text while reformatting. I have notified Juraj.

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채택된 답변

Lucas García
Lucas García 2011년 9월 1일
[Updated]
Define the symbolic variables as real and use the function simplify when needed:
>> syms a b c d real;
>> F=a+j*b; G=c+j*d;
imF=imag(F)
imF =
b
>> D = F/G;
imag(D)
ans =
((a - b*i)*i)/(2*(c - d*i)) - ((a + b*i)*i)/(2*(c + d*i))
>> simplify(imag(D))
ans =
-(a*d - b*c)/(c^2 + d^2)
  댓글 수: 5
Walter Roberson
Walter Roberson 2011년 9월 2일
Also sometimes it helps to expand() and then simplify() again.
When working with imaginary values in Maple, sometimes I find I can make significant simplifications by simplify(combine(convert(EXPRESSION,expln))) and then converting back to real + i*imaginary format. Unfortunately I have not managed to find the MuPad equivalents of Maple's convert() or combine() functions.
Walter Roberson
Walter Roberson 2017년 11월 3일
From R2012a, rewrite() can be used to do some conversions; from R2014a, combine() can be used to combine operations.

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추가 답변 (1개)

Modess Seyednezhad
Modess Seyednezhad 2017년 11월 3일
But I got this:
>> syms a b c d real; F=a+j*b; G=c+j*d; imF=imag(F)
imF =
b
>> D = F/G; >> k=imag(D)
k =
(b*c)/(c^2 + d^2) - (a*d)/(c^2 + d^2)
????
  댓글 수: 1
Steven Lord
Steven Lord 2017년 11월 3일
And that expression for k is equivalent to the expression Juraj expected. Either simplify k or use numden to extract the numerator and denominator of k and it should match your expectation.

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