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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 :

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

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

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

113 Views

70.
Find the modulus of the following complex numbers :
(2+3i)(1-i)+(3-5i)

Let             z = (2+3i)(1-i)+(3-5i) = (2 - 2i + 3i -3i²) + ( 3 -5i)
                    = (5+i) + (3-5i) = 8 -4i

$rightwards double arrow$ $space space space space space space space space space space space space space space space open vertical bar straight z close vertical bar space equals space square root of left parenthesis 8 right parenthesis squared space plus space left parenthesis negative 4 right parenthesis squared end root$

        $space space space space space space space space space space space space space space equals space space square root of 64 plus 16 end root space equals space square root of 80 space equals space 4 square root of 5$