document.write( "Question 230805: find a complex number such that radical i = a+bi. \n" ); document.write( "

Algebra.Com's Answer #170935 by Alan3354(69443) $\"\"$ $\"About$

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radical i = a+bi.
\n" ); document.write( " $\"sqrt%28i%29+=+a%2Bbi\"$
\n" ); document.write( "square both sides
\n" ); document.write( " $\"i+=+a%5E2+-+b%5E2+%2B+2abi\"$
\n" ); document.write( "2ab = 1 --> a = 1/(2b)
\n" ); document.write( "a^2 = b^2
\n" ); document.write( "1/(4b^2) = b^2
\n" ); document.write( "4b^4 = 1
\n" ); document.write( "a = b = 1/2
\n" ); document.write( "a = b = -1/2
\n" ); document.write( "a = b = 2 complex roots, also \n" ); document.write( "

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