document.write( "Question 1144069: Verify that sqrt2|z|≤|Re(z)|+|Im(z)| \n" ); document.write( "

Algebra.Com's Answer #765112 by ikleyn(52908) $\"\"$ $\"About$

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document.write( "Hello, I do understand what is written in the right side of this inequality.\r\n" );
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document.write( "    > > >  But I do not understand what is written in its left side.  < < <\r\n" );
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document.write( "If it is  \r\n" );
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document.write( "     sqrt(2) * |z| <= |Re(z)| + |Im(z)|,      (1)\r\n" );
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document.write( "then I can easily disprove it:  take  z = 1 = 1 + 0*i;\r\n" );
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document.write( "                                Then  sqrt(2) * |z| = sqrt(2) in the left side \r\n" );
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document.write( "                                and  |Re(z)| + |Im(z)| = 1 + 0 = 1,\r\n" );
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document.write( "                                so the inequality (1) is not correct in this case.\r\n" );
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document.write( "If it is  \r\n" );
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document.write( "     sqrt((2)*|z|) <= |Re(z)| + |Im(z)|,      (2)\r\n" );
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document.write( "then I can easily disprove it, again:  \r\n" );
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document.write( "                                take  z = 1 = 1 + 0*i;\r\n" );
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document.write( "                                Then  sqrt((2) * |z|) = sqrt(2) in the left side \r\n" );
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document.write( "                                and  |Re(z)| + |Im(z)| = 1 + 0 = 1 in the right side,\r\n" );
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document.write( "                                so the inequality (2) is not correct in this case, too.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Could you PLEASE write your post / posts more ACCURATELY, in a way the tutors do not spend their time for NOTHING,
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