Why matlab only fives one complex result?

Hello everyone, I have been struggling for so much time...I have been doing a complex equation (I am actually able to solve it manually but I just want to ger more familiar with Matlab). There are 3 complex solutons, however, matlab only gives me one of them. What can I do so that it gives me all 3 solutions?

Answer 1

[Walter Roberson]

Square both sides of the equation. MATLAB will provide 3 solutions.

It is advisable to cross check the solutions, as squaring both sides can introduce false roots.

[Walter Roberson]

>> syms z
>> solve((z^(-3/2))^2 == (3-3*i)^2)
ans =
                         (1i/18)^(1/3)
  (1i/18)^(1/3)*((3^(1/2)*1i)/2 - 1/2)
 -(1i/18)^(1/3)*((3^(1/2)*1i)/2 + 1/2)
>> simplify(solve((z^(-3/2))^2 == (3-3*i)^2))
ans =
                           ((-1)^(1/6)*18^(2/3))/18
 ((-1)^(1/6)*2^(2/3)*3^(1/3)*(- 1 + 3^(1/2)*1i))/12
  -((-1)^(1/6)*2^(2/3)*3^(1/3)*(1 + 3^(1/2)*1i))/12
>> double(ans)
ans =
          0.330450538041682 +     0.190785707092222i
         -0.330450538041682 +     0.190785707092222i
                          0 -     0.381571414184444i
>> ans.^(-3/2)
ans =
                          3 -                     3i
                         -3 +                     3i
                         -3 +                     3i
                         

Cross-check shows there is only one solution. The claim that there are 3 solutions is incorrect.

[Graciano Ding]

Just one question...how can (0-0.381571414184444i)^(-3/2) be -3+3*i? I calculated it manually and it should be one of the answers...what mistake did I make?

Answer 2

[Sai Bhargav Avula]

Hi,

MATLAB cannot generate all the Solutions, which might require a global solver.

However, if you have the Extended Symbolic Math Toolbox (access to Maple), then you can do this in Maple.

maple('_EnvAllSolutions:= true;')

This can give a generic result for the equation provided

[Walter Roberson]

This is misleading. Producing all of the solutions does not require a global solver.

[Sai Bhargav Avula]

It might require different intilizations to get all the solutions. So I suggested this.