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Relations And Functions

Question
CBSEENMA11013086
Wired Faculty App

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

Solution
space space space space space space space fraction numerator 3 plus 4 straight i over denominator 1 minus 2 straight i end fraction equals left parenthesis 3 plus 4 straight i right parenthesis fraction numerator left parenthesis 1 plus 2 straight i right parenthesis over denominator left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end fraction                   space space space space space space space space space space space open parentheses because fraction numerator 1 over denominator straight a plus ib end fraction equals fraction numerator straight a minus ib over denominator straight a squared plus straight b squared end fraction close parentheses

space space space space space space space space space space space equals space space space fraction numerator left parenthesis 3 plus 4 straight i right parenthesis left parenthesis 1 plus 2 straight i right parenthesis over denominator 5 end fraction equals fraction numerator 3 plus 10 straight i plus 8 straight i squared over denominator 5 end fraction equals fraction numerator negative 5 plus 10 straight i over denominator 5 end fraction equals negative 1 plus 2 straight i
rightwards double arrow      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 top enclose open parentheses negative 1 plus 2 straight i close parentheses end enclose space equals space minus 1 minus 2 straight i                                                   ....(i)
Also,      <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) #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>
     space space space space space space equals space fraction numerator negative 5 minus 10 straight i over denominator 5 end fraction equals negative 1 minus 2 straight i                                                                       ....(ii)
Hence, from (i) and (ii),    space space space space space space space 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 top enclose fraction numerator open parentheses 3 plus 4 straight i close parentheses over denominator top enclose open parentheses 1 minus 2 straight i close parentheses end enclose end fraction end enclose

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Some More Questions From Relations and Functions Chapter

Collection of beautiful girls in India.

Fill in the blanks in the following table:

Numbers

Closed under
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

  

No

Integers

  

Yes

  

No

Whole numbers

...

  

Yes

  

Natural numbers

  

No

    
 

i9 + i19

3(7 + i7) + i(7 + i7)

Express each of the complex number given in the  form of  a + ib.

(1 - i) - (-1 + i6)

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