document.write( "Question 887983: the maximum value of |z| when z satisfies the condition |z+2/z|=2 is \n" ); document.write( "
Algebra.Com's Answer #537017 by rothauserc(4718)\"\" \"About 
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we have two cases to consider
\n" ); document.write( "1) z +2/z = 2
\n" ); document.write( "multiply both sides of = by z (note that z not = 0)
\n" ); document.write( "z^2 +2 = 2z
\n" ); document.write( "z^2 -2z = -2
\n" ); document.write( "complete the square
\n" ); document.write( "z^2 -2z +1 = -2 +1
\n" ); document.write( "(z -1)^2 = -1
\n" ); document.write( "z -1 = square root(-1)
\n" ); document.write( "z = 1 +i (note that square root -1 is i)
\n" ); document.write( "2) -(z +2/z) = 2
\n" ); document.write( "multiply both sides of = by -
\n" ); document.write( "z +2/z = -2
\n" ); document.write( "multiply both sides of = by z
\n" ); document.write( "z^2 +2 = -2z
\n" ); document.write( "z^2 +2z = -2
\n" ); document.write( "complete the square
\n" ); document.write( "z^2 +2z +1 = -2 +1
\n" ); document.write( "(z +1)^2 = -1
\n" ); document.write( "take square root of both sides of =
\n" ); document.write( "z +1 = square root(-1)
\n" ); document.write( "z = i - 1
\n" ); document.write( "therefore z = i-1 or 1+i
\n" ); document.write( "note that |a +bi | = square root(a^2 +b^2)
\n" ); document.write( "|z| = |i - 1| = square root(1 +1) = square root(2)
\n" ); document.write( "|z| = (1 +i| = square root(1 +1) = square root(2)
\n" ); document.write( "|z| = square root(2) or -square root(2)
\n" ); document.write( "we choose the positive square root(2)
\n" ); document.write( "|z| = square root(2)\r
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