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Complex Numbers and Quadratic Equations

Short Answer Type

71.

Find the modulus of the following complex numbers :

$space space space space fraction numerator 3 minus 4 straight i over denominator 4 minus 3 straight i end fraction$

107 Views

72.
Find the modulus of the following complex numbers :

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space space space space space space space space space space space space space space space space space space space space straight z equals fraction numerator open parentheses 2 plus 3 straight i close parentheses over denominator 1 minus 3 straight i end fraction equals fraction numerator left parenthesis 2 plus 3 straight i right parenthesis left parenthesis 2 plus 3 straight i right parenthesis over denominator 1 minus 3 straight i end fraction

rightwards double arrow

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space space space space space space space space space space equals 1 over 10 left parenthesis 13 square root of 10 right parenthesis

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111 Views

73.

Solve x²+ 3 = 0

127 Views

74.

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

135 Views

75.

Conver $straight pi over 12$ to degrees.

115 Views

76.

Write the complex number $space space space space space space space space fraction numerator straight i minus 1 over denominator cos begin display style straight pi over 3 end style plus space straight i space sin begin display style straight pi over 3 end style end fraction$ in the polar form.

119 Views

77.

Write the conjugate of z = – 3 – 21

129 Views

78.

Find the value of the following : $space space space space open parentheses 1 plus straight i close parentheses to the power of 4 open parentheses 1 plus 1 over straight i close parentheses to the power of 4$

133 Views

Multiple Choice Questions

79.

The sum of all real values of x satisfying the equation
$left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 space equals space 1 end exponent$ is:

3
-4
6
6

654 Views

80.

A complex number z is said to be unimodular, if |z|= 1. suppose z₁ and z₂ are complex numbers such that $fraction numerator straight z subscript 1 minus 2 straight z subscript 2 over denominator 2 minus straight z subscript 1 begin display style stack straight z subscript 2 with minus on top end style end fraction$ is unimodular and z₂ is not unimodular. Then, the point z₁ lies on a