Relations and Functions

Relations and Functions

Question

find the smallest positive integer n for which space space space space space open parentheses fraction numerator 1 plus straight i over denominator 1 minus straight i end fraction close parentheses to the power of straight n equals space 1

Answer

We are given that  space space space space space space space space open parentheses fraction numerator 1 plus straight i over denominator 1 minus straight i end fraction close parentheses to the power of straight n equals 1
space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space space space space space space space space space space space space space space space space space open parentheses fraction numerator 1 plus straight i over denominator 1 minus straight i end fraction straight x fraction numerator 1 plus straight i over denominator 1 plus straight i end fraction close parentheses to the power of straight n equals 1 rightwards double arrow open square brackets fraction numerator 1 plus straight i squared plus 2 straight i over denominator 1 squared minus straight i squared end fraction close square brackets to the power of straight n equals 1 rightwards double arrow open parentheses fraction numerator 2 straight i over denominator 2 end fraction close parentheses to the power of straight n equals 1
         space space space space space space space rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space straight i to the power of straight n equals 1 equals straight i to the power of 4
                 ( The least positive integral power of i which makes it equal to 1 is 4)
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#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>

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