How to find values for these variables?












0












$begingroup$


I have four unknowns and one equation. Is there a way to assign non-trivial values to them?



The variables are: $$q_0, q_1 in [0, 1] \ e_0, e_1 in [{z in mathcal{C} :
lvert z rvert le 1}]$$



And the equation is:
$$q_0 times sqrt{1 - q_1^2} times e_1 + q_1 times sqrt{1 - q_0^2} times e_0^{text{*}} = 0$$



$e_i$s are complex numbers. I can't figure out whether there is a way to assign values that would satisfy the equation. Any ideas?



Thanks.






complex-numbers systems-of-equations absolute-value satisfiability







share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    I have four unknowns and one equation. Is there a way to assign non-trivial values to them?



    The variables are: $$q_0, q_1 in [0, 1] \ e_0, e_1 in [{z in mathcal{C} :
    lvert z rvert le 1}]$$



    And the equation is:
    $$q_0 times sqrt{1 - q_1^2} times e_1 + q_1 times sqrt{1 - q_0^2} times e_0^{text{*}} = 0$$



    $e_i$s are complex numbers. I can't figure out whether there is a way to assign values that would satisfy the equation. Any ideas?



    Thanks.






    complex-numbers systems-of-equations absolute-value satisfiability







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I have four unknowns and one equation. Is there a way to assign non-trivial values to them?



      The variables are: $$q_0, q_1 in [0, 1] \ e_0, e_1 in [{z in mathcal{C} :
      lvert z rvert le 1}]$$



      And the equation is:
      $$q_0 times sqrt{1 - q_1^2} times e_1 + q_1 times sqrt{1 - q_0^2} times e_0^{text{*}} = 0$$



      $e_i$s are complex numbers. I can't figure out whether there is a way to assign values that would satisfy the equation. Any ideas?



      Thanks.






      complex-numbers systems-of-equations absolute-value satisfiability







      share|cite|improve this question









      $endgroup$




      I have four unknowns and one equation. Is there a way to assign non-trivial values to them?



      The variables are: $$q_0, q_1 in [0, 1] \ e_0, e_1 in [{z in mathcal{C} :
      lvert z rvert le 1}]$$



      And the equation is:
      $$q_0 times sqrt{1 - q_1^2} times e_1 + q_1 times sqrt{1 - q_0^2} times e_0^{text{*}} = 0$$



      $e_i$s are complex numbers. I can't figure out whether there is a way to assign values that would satisfy the equation. Any ideas?



      Thanks.






      complex-numbers systems-of-equations absolute-value satisfiability




      complex-numbers systems-of-equations absolute-value satisfiability






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 13 at 16:02









      Hasan IqbalHasan Iqbal

      1267




      1267






















          0






          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3072152%2fhow-to-find-values-for-these-variables%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes
















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid …



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3072152%2fhow-to-find-values-for-these-variables%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          MongoDB - Not Authorized To Execute Command

          Image
          .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 I have successfully enabled authorization on MongoDB and I have created an account on the admin database and then I created an account for my database called test. The following connection string to connect to my test database works successfully: mongo --host 192.168.17.52 --port 27017 -u user1 -p password --authenticationDatabase test Only problem I have now is, I cannot execute commands such as: show dbs. I get the following error when I try to do so: "errmsg" : "not authorized on admin to execute command { listDatabases: 1.0, lsid: { id: UUID("a1d5bc0d-bc58-485e-b232-270758a89455") }, $db: "admin...
          Read more

          How to fix TextFormField cause rebuild widget in Flutter

          Image
          .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 I've got the same issue at #9280. I tried all solutions from that topic with/without GlobalKey for Scaffold and Form but the problem wasn't fixed. I tried to build a authentication form with login and signup. But the keyboard doesn't show when I tap the TextFormField at the first time. Then I try to input some letter from physical keyboard, the widget is rebuilt. Like this: login screen Nothing to be log when I run flutter run --verbose, so I logged manually. Every tapping on field, the widget called dispose -> init -> build. [√] Flutter (Channel beta, v1.0.0, on Microsoft Windows [Version 10.0.17763.195], ...
          Read more

          Npm cannot find a required file even through it is in the searched directory

          Image
          up vote 0 down vote favorite I got that error: users-Air:pdfuploader user$ npm run start client@0.1.0 start /Users/user/Documents/pdfuploader react-scripts start Could not find a required file. Name: index.html Searched in: /Users/user/Documents/pdfuploader/public npm ERR! code ELIFECYCLE npm ERR! errno 1 npm ERR! client@0.1.0 start: `react-scripts start` npm ERR! Exit status 1 npm ERR! npm ERR! Failed at the client@0.1.0 start script. npm ERR! This is probably not a problem with npm. There is likely additional logging output above. npm ERR! A complete log of this run can be found in: npm ERR! /Users/user/.npm/_logs/2018-11-19T10_19_14_555Z-debug.log users-Air:pdfuploader user$ And the file is in /Users/user/Documents/pdfuploader/public as you can see in my github repository: https://github.c...
          Read more