document.write( "Question 1155809: Let z=a + bi. Discuss the values of a and b so that the following is true: z (i) is a positive real number. \n" ); document.write( "
Algebra.Com's Answer #778485 by ikleyn(52775)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "It can be solved writing equations, but as an alternative, can be solved mentally, if you just know the properties of complex numbers.\r
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document.write( "    In order for z*(i) is a positive real number, \r\n" );
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document.write( "    it is necessary and sufficient that the number z be the complex conjugate to \"i\", multiplied by any positive real number.\r\n" );
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document.write( "    In other words, the set of complex numbers, satisfying the given condition, \r\n" );
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document.write( "    is   {z | z = -r*i},  where \"r\" is any positive real number.\r\n" );
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document.write( "     It means that in the form z = a + bi,  \"a\" is equal to zero and \"b\" is any negative real number.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On complex numbers, see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Complex numbers and arithmetical operations on them\r
\n" ); document.write( "\n" ); document.write( "    - Complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Addition and subtraction of complex numbers in complex plane\r
\n" ); document.write( "\n" ); document.write( "    - Multiplication and division of complex numbers in complex plane\r
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\n" ); document.write( "\n" ); document.write( "    - Solved problems on taking roots of complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic operations on complex numbers\r
\n" ); document.write( "\n" ); document.write( "    - Solved problem on taking square root of complex number\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Complex numbers\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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