document.write( "Question 1208271: If z1 and z2 are complex numbers and |z2| = 4 , |z1|+ i×|z2|= 3 + 4i , then value of |z2 + i × z1|=...
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Algebra.Com's Answer #846581 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "If z1 and z2 are complex numbers and |z2| = 4 , |z1|+ i×|z2|= 3 + 4i , then value of |z2 + i × z1|=...
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document.write( "Read the problem attentively.  It says that  |z1|+ i×|z2| = 3 + 4i.\r\n" );
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document.write( "This means that  |z1| = 3,  |z2| = 4.\r\n" );
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document.write( "Now, due to the \"triangle\" inequality for adding complex number, \r\n" );
document.write( "the general rule is that for all complex numbers z1 and z2\r\n" );
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document.write( "    |z2 + z1| <= |z2| + |z1|.\r\n" );
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document.write( "Hence, in your case,  |z2 + i*z1|  can not be greater than 4 + 3 = 7.\r\n" );
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document.write( "Thus, options  9, 16, 25 do not work.\r\n" );
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document.write( "The only acceptable option is the remaining value of 5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "This problem is a Math joke on complex numbers.\r
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