Relations And Functions

  • Question
    CBSEENMA11013030

    If (a + ib) (c+id)(e+if)(g+ih) = A+iB, then show that : (a2 + b2) (c2 + d2 ) (e2 + f2 ) (gh2 ) = A2 + B2

    Solution

    Here, (a + ib) (c+id)(e+if)(g+ih) = A+iB
    Taking modulus, on both sides, we get
    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#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>
    rightwards double arrow space space space space space space space space space space space space space space open vertical bar straight a plus space ib close vertical bar space open vertical bar straight c space plus space id close vertical bar space open vertical bar straight e plus if close vertical bar space open vertical bar straight g plus ih close vertical bar space space space equals space open vertical bar straight A plus iB close vertical bar<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#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> 

    space space space square root of straight a squared plus straight b squared end root space square root of straight c squared plus straight d squared space end root space square root of straight e squared plus straight f squared end root space square root of straight g squared plus straight h squared space end root space space space equals space space square root of straight A squared plus straight B squared end rootspace space space space open square brackets because space straight z space equals space straight a plus ib rightwards double arrow open vertical bar straight z close vertical bar equals space square root of straight a squared plus straight b squared end root close square brackets
    Squaring both sides, we get
    space space space space space space space space space space space space open parentheses square root of open parentheses straight a squared plus straight b squared close parentheses space space open parentheses straight c squared plus straight d squared close parentheses open parentheses straight e squared plus straight f squared close parentheses open parentheses straight g squared plus straight h squared close parentheses end root close parentheses to the power of 2 space space space end exponent space space space space space equals space space space space space space space space space open parentheses square root of straight A squared plus straight B squared end root close parentheses squared
    rightwards double arrow       (a2 + b2) (c2 + d2 ) (e2 + f2 ) (gh2 ) = A2 + B2

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