Need Help with a Simple Symbolic Equation Solve in Matlab 2015a
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I am trying the following code in Matlab 2015a. It cannot solve it. Correct solution should be simply k. Could you tell me what is wrong?
syms Z k
assume(Z,'real')
assume(k,'real')
[Z]=solve(abs(k/(k+1i*Z))==1/sqrt(2));
Z=????
2 Comments
Roger Stafford
on 24 Jul 2015
Without your assumptions that k and Z are real, the solution for any given k would be Z = w*k where w = x+1i*y is any point on the circle in the complex plane:
x^2 + (y-1)^2 = 2
In other words there would be an infinite continuum of possible solutions and 'solve' could not give you an answer.
Given that k and Z must be real, the solution is thereby restricted to the two points, Z = k and Z = -k, where the circle crosses the real line, so that 'solve' could and should have given you that answer. I suspect that the combination of the given assumptions together with the 'abs' operator confused Mathworks' 'solve' to the point where it was unable to give this simple answer.
Answers (4)
Sean de Wolski
on 24 Jul 2015
One equation with two unknowns. What do you expect?
Torsten's suggestion gives you the result for Z:
ZZ = solve(abs(k/(k+1i*Z))==1/sqrt(2),Z);
ZZ = k*1i - 2^(1/2)*exp(z*2i)*abs(k)*1i
But it will of course include k because you have two unknowns.
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