title: Force maxima to think square root is imaginary
body: <p>I wanted to see how an elliptic trajectory of a dynamical system gets rotated with different system parameters.  So I tried</p>
  
  <pre><code>assume(c&lt;0);
  assume(b&gt;0);
  assume(b*c&lt;-a^2);
  A:matrix([a,b],[c,-a]);
  eigenvalues(A);
  </code></pre>
  
  <p>I get the result</p>
  
  <pre><code>[[-sqrt(b*c+a^2),sqrt(b*c+a^2)],[1,1]]
  </code></pre>
  
  <p>However, I want</p>
  
  <pre><code>[[-%i*sqrt(a^2+b*c),%i*sqrt(a^2+b*c)],[1,1]]
  </code></pre>
  
  <p>It appears that maxima did not use my assumption. How can I make it use such an assumption or do I need to do it manually?</p>