document.write( "Question 1115020: Let z=a+bi. Discuss the values of a and b so that the following will be true:
\n" ); document.write( "z(i) is a positive real number and z(3-i) is a pure imaginary number. \n" ); document.write( "

Algebra.Com's Answer #729949 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"z%2Ai=%28a%2Bbi%29%2Ai\"$
\n" ); document.write( " $\"z%2Ai=a%2Aii%2Bb%2Ai%5E2\"$
\n" ); document.write( " $\"z%2Ai=-b%2Bai\"$
\n" ); document.write( "For this to be real and positive,
\n" ); document.write( " $\"b%3C0\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"z%2A%283-i%29=%28a%2Bbi%29%2A%283-ii%29\"$
\n" ); document.write( " $\"z%2A%283-i%29=3a-ai%2B3bi-bi%5E2\"$
\n" ); document.write( " $\"z%2A%283-i%29=%283a%2Bb%29%2B%283b-a%29i\"$
\n" ); document.write( "For this to be imaginary,
\n" ); document.write( " $\"3a%2Bb=0\"$
\n" ); document.write( "and
\n" ); document.write( " $\"3b-a%3C%3E0\"$
\n" ); document.write( " \n" ); document.write( "

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