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Complex Numbers and Quadratic Equations

Short Answer Type

51.

Write the conjugates of the following complex numbers :

$space space space space space space space square root of negative 16 end root space minus space square root of negative 9 end root space straight i$

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52.

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

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53.
If z = -5 + 2i and $space space space space top enclose straight z space equals space 5 straight x space minus space 4 yi$ , find values of x and y.

z = -5 + 2i ...(i)

$rightwards double arrow$ $space space space top enclose straight z space equals space minus 5 space minus 2 straight i space$ ...(ii)

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

From (iii) and (vi), -5 -5i = 5x - 4yi

Eqating real and imaginary parts, we get.

 5x - 5 $rightwards double arrow$ x = -1

and - 4y = -2 $rightwards double arrow$ y = $space space 1 half$

Hence, x = -1 and y = $1 half$

131 Views

54.

Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

128 Views

55.

Z₁= 5 - 3i, Z₂ = 2 +4i, find Z₁ + Z_2.

112 Views

56.

Find x and y if : (2x + iy) + (-3 + 2i) = 3i

115 Views

57.

Find the additive inverse of Z = -3 + 2i.

149 Views

58.
find the multiplicative inverse of Z = 2 -3i.

361 Views

59.

Write the following in the form a + ib.

$space space space space space space fraction numerator 1 over denominator 3 space plus space 4 straight i end fraction$

118 Views

60.

Write the following in the form a + ib.

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

94 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

53. If z = -5 + 2i and , find values of x and y.

53.
If z = -5 + 2i and $space space space space top enclose straight z space equals space 5 straight x space minus space 4 yi$ , find values of x and y.