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Complex Numbers and Quadratic Equations

Short Answer Type

61.

Write the following in the form a + ib.

$space space space space space space fraction numerator 1 minus 2 straight i over denominator left parenthesis 2 plus 3 straight i right parenthesis squared end fraction space$

102 Views

62.

Find the multiplicative inverse of the following complex numbers :

$space space space space space space space space space space space 4 minus square root of negative 9 end root$

110 Views

63.

Find the multiplicative inverse of the following complex numbers :

$space space space space space space space space space space space space space space space space fraction numerator left parenthesis 2 plus 3 straight i right parenthesis space left parenthesis 3 space plus 2 straight i right parenthesis over denominator 5 space plus space straight i end fraction$

112 Views

64.
Find the multiplicative inverse of :

$space space space space space space space space space space space space straight z space equals space cos space straight theta space minus space 1 space sin space straight theta$

Multiplicative inverse of

$space space space space space space space space space space space space space space space straight z space equals space 1 over straight z space equals space fraction numerator 1 over denominator cos space straight theta space minus straight i space sin space straight theta end fraction space equals space fraction numerator 1 over denominator cosθ space minus space straight i space sin space straight theta end fraction. fraction numerator cos space straight theta space plus space straight i space sin space straight theta over denominator cos space straight theta space plus space straight i space sin space straight theta end fraction$

$space space space space space space space space space space space space space equals space space space fraction numerator cos space straight theta space plus space straight i space sin space straight theta over denominator cos squared space straight theta space minus space straight i squared space sin squared space straight theta end fraction space equals space fraction numerator cos space straight theta space plus space straight i space sin space straight theta over denominator cos squared space straight theta plus sin squared space straight theta end fraction equals fraction numerator cos space straight theta space plus space straight i space sin space straight theta over denominator 1 end fraction$

$space space space space space space space equals space cosθ plus space straight i space sinθ$

107 Views

65.

Find the multiplicative inverse of :

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

98 Views

66.

Find the square root of the following complex numbers :

-5 + 12i

108 Views

67.

Find the square root of the following complex numbers :

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

112 Views

68.

Verify that $space space space space space space top enclose left parenthesis 2 plus 3 straight i right parenthesis left parenthesis straight i minus 2 straight i right parenthesis end enclose space equals space top enclose left parenthesis 2 plus 3 straight i right parenthesis space end enclose space. space top enclose left parenthesis 1 minus 2 straight i right parenthesis end enclose space space$

132 Views

69.

Verify that

$space space space space space space space space space space space space space top enclose open parentheses fraction numerator 3 plus 4 straight i over denominator 1 minus 2 straight i end fraction close parentheses end enclose space equals space fraction numerator top enclose open parentheses 3 plus 4 straight i close parentheses end enclose over denominator top enclose open parentheses 1 minus 2 straight i close parentheses end enclose end fraction$