title: Mathematica: Show Complex Numbers in Polar Form
body: <p>I want to display complex numbers in trig form. For example:</p>
  <pre><code>z = (-4)^(1/4);
  </code></pre>
  <p>I'm not sure what the command for that is, and its silly to write:</p>
  <p><img src="https://i.stack.imgur.com/WmiE6.png" alt="alt text" /></p>
  <p>I thought, that the command was <code>ExpToTrig</code>, but solution can't possibly be just <code>1+i</code> (Or can it, and I'm misusing it?). How do display complex number in trig form.</p>
  <h3>Edit:</h3>
  <p>Command is <code>ExpToTrig</code>, it just does not give all the solutions (or i have failed to find out how). Finally solved my problem with writing a pure function <code>NrootZpolar[n][z]</code>:</p>
  <pre><code>NrootZpolar := 
   Function[x, 
    Function[y, 
         ( Abs[y] ^ (1/x) *
         ( Cos[((Arg[y] + 360° * Range[0, x - 1]) / x)] + 
         I*Sin[((Arg[y] + 360° * Range[0, x - 1]) / x)]))
    ]
   ]
  </code></pre>
  <p>And use:</p>
  <pre><code>In[689]:= FullSimplify[NrootZpolar1[4][-4]]
  Out[689]= {1 + I, -1 + I, -1 - I, 1 - I}
  </code></pre>
  <p>To visualize:</p>
  <pre><code>ComplexListPlot[list_] := ListPlot[Transpose[{Re[list], Im[list]}], AxesLabel -&gt; {Re, Im}, PlotLabel -&gt; list, PlotMarkers -&gt; Automatic]
  Manipulate[ComplexListPlot[FullSimplify[NrootZpolar1[n][z]]], {z, -10, 10}, {n, 1, 20}]
  </code></pre>
  <p><img src="https://i.stack.imgur.com/9nwFs.gif" alt="alt text" /></p>