title: Mathematica solving complex equation
body: <p>If I have a complex equation in the form of</p>
  
  <pre><code>   Solve[z^2 + 9 - 1.5 E^[-tz]==0, z]
     where z = x + I y
     where x , y  and t are all assumed to be real.
  </code></pre>
  
  <p>How do I tell Mathematica 9 to separate the real and imaginary parts to make
  two equations in the form of </p>
  
  <pre><code>   Re[z]==0, Im[z]==0.
  </code></pre>
  
  <p>I try this  </p>
  
  <pre><code>    myConjugate[eqn_Equal] := myConjugate /@ eqn
      myConjugate[expr_] := expr /. {I -&gt; -I, a_Complex :&gt; Conjugate[a]}
      myRe[eqn_Equal] := myRe /@ eqn
      myRe[expr_] := (expr + myConjugate[expr])/2
      myIm[eqn_Equal] := myIm /@ eqn
      myIm[expr_] := (expr - myConjugate[expr])/(2 I)
  </code></pre>
  
  <p>and   </p>
  
  <pre><code>{myRe[#], myIm[#]} &amp;[(x + I y)^2 + 9 - 1.5 E[- t (x+ I y)] == 0]
  </code></pre>