Relations and Functions

Relations and Functions

Question

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

Answer

Here, (a + ib) (c+id)(e+if)(g+ih) = A+iB
Taking modulus, on both sides, we get
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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)
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#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)
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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)
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#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)
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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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