solving equation in complex vaariables

Question

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How can I solve z(z-1)=1 using MATLAB. z is a complex variable. Is there any direct method? I did it separating the real part and imaginary part.

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Answer 1

Walter Roberson 2011-7-23

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Expand the expression:

z*(z-1)=1
z^2-z=1
z^2-z-1=0

This is a quadratic equation which can be solved by standard methods,

roots([1,-1,-1])

You will find that the solutions have no imaginary components.

R yan 2011-7-23

Thanks for your answer. But for any general equation in Z, does MATLAB has a direct solver?

Walter Roberson 2011-7-23

No. There is no direct solver that is suitable for "any general equation" even in reals.

The Symbolic Toolbox is able to solve a fair variety of equations over complex numbers.

The only general solving routine outside of the Symbolic Toolbox that I have found that is able to handle complex numbers directly, is fgoalattain()