document.write( "Question 1034205: i know i^2 =-1 so i^26 must be -1. but i can write i^26 as (i^4)^(26/4) and we know i^4 is 1 so it is 1. my question is what is my mistake here? \r
\n" ); document.write( "\n" ); document.write( "and can i write (i)3/2 as (i^3)^(1/2) and i^3 = -i so it turns to (−i)^(1/2). is it right? \r
\n" ); document.write( "\n" ); document.write( "and if the last is wrong how could i find the answer. \n" ); document.write( "

Algebra.Com's Answer #648860 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Fractional exponents must be avoided in mathematics courses \r\n" );
document.write( "less advanced than complex analysis.  In complex analysis \r\n" );
document.write( "there are \"multi-valued functions\".\r\n" );
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document.write( "There are two square roots of, say, 4, +2 and -2.\r\n" );
document.write( "However, in math courses less advanced than complex analysis,\r\n" );
document.write( "we restrict the symbol  to mean only the positive\r\n" );
document.write( "square root of 4, not -2.  If we want the other square root,\r\n" );
document.write( "-2, we must write .  That agreement was made \r\n" );
document.write( "so that the square root relation would be a function, passing \r\n" );
document.write( "the vertical line test.\r\n" );
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document.write( "But imaginary (complex) numbers are neither positive nor \r\n" );
document.write( "negative, so no such agreement is possible.  +i is neither a \r\n" );
document.write( "positive number nor a negative number. Likewise -i is neither\r\n" );
document.write( "a negative number nor a positive number. \r\n" );
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document.write( "So  \r\n" );
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document.write( "and its equivalent expression \r\n" );
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document.write( "actually is double valued and means both the values,\r\n" );
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document.write( "but that is in the more advanced course complex analysis.\r\n" );
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document.write( "Until we study the advanced mathematics course of complex\r\n" );
document.write( "analysis, we must avoid writing radicals or fraction\r\n" );
document.write( "exponents of negative or imaginary numbers.\r\n" );
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document.write( "Therefore  may not be written as \r\n" );
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document.write( "in lower math courses because it involves a fractional \r\n" );
document.write( "exponent of an imaginary number.\r\n" );
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document.write( "Edwin

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