document.write( "Question 27172: I am trying to find out if these are true:
\n" ); document.write( " $\"%281+%2B+i%29+%2F+sqrt+%282%29+=+sqrt+%28i%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%281+-+i%29+%2F+sqrt+%282%29+=+sqrt+%28-i%29\"$
\n" ); document.write( "I can verify
\n" ); document.write( " $\"%28%281+%2B+i%29+%2F+sqrt+%282%29%29%5E2+=+i\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%28%281+-+i%29+%2F+sqrt+%282%29%29%5E2+=+-i\"$
\n" ); document.write( "The following should be true, but I can't seem to prove it
\n" ); document.write( "
\n" ); document.write( "I run into a sign problem- keep getting +1 = -1
\n" ); document.write( "Thanks for your help \n" ); document.write( "

Algebra.Com's Answer #15096 by venugopalramana(3286) $\"\"$ $\"About$

You can put this solution on YOUR website!
GLAD TO NOTE YOUR SINCERE DESIRE TO LEARN AN IMPORTANT CONCEPT,WHICH IF NOT UNDERSTOOD PROPERLY MAY LEAD TO FALLACY.
\n" ); document.write( "THE PROBLEM ARISES WHEN ONE TRIES TO COMBINE RULES FOR REAL NUMBERS WITH THOSE FOR COMPLEX NUMBERS.TO SUM UP
\n" ); document.write( " $\"%28sqrt%28a%29%29\"$ * $\"%28sqrt%28b%29%29\"$ = $\"%28sqrt%28a%2Ab%29%29\"$ IS ONLY TRUE IF ATLEAST ONE OF a OR b IS POSITIVE.OTHERWISE WHEN BOTH ARE NEGATIVE ,YOU SHOULD CALCULATE IT USING COMPLEX NUMBERS AS FOLLOWS
\n" ); document.write( "LET US DO WITH AN EXAMPLE PUTTING NUMBERS FOR a AND b.
\n" ); document.write( " $\"%28sqrt%28-4%29%29\"$ * $\"%28sqrt%28-9%29%29\"$ = $\"%28sqrt%28%28-4%29%2A%28-9%29%29%29\"$ IS NOT CORRECT AS BOTH NUMBERS ARE NEGATIVE..IT LEADS TO ABSURD RESULT OF
\n" ); document.write( "LHS=2i*3i=6i^2=-6.....RHS=+6...THAT IS -6=+6....ABSURD
\n" ); document.write( "THE PROPER WAY OF DOING IN SUCH CASES IS WHAT IS DONE ON THE LHS,THAT IS USING COMPLEX NUMBERS 2i*3i=6i^2=-6......
\n" ); document.write( " HOPE IT IS CLEAR..NOW YOU CAN EASILY SEE WHERE YOU HAVE DONE CORRECTLY AND WHERE YOU ERRED....
\n" ); document.write( "I am trying to find out if these are true:
\n" ); document.write( " $\"%281+%2B+i%29+%2F+sqrt+%282%29+=+sqrt+%28i%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%281+-+i%29+%2F+sqrt+%282%29+=+sqrt+%28-i%29\"$
\n" ); document.write( "I can verify
\n" ); document.write( " $\"%28%281+%2B+i%29+%2F+sqrt+%282%29%29%5E2+=+i\"$ ....VERY GOOD ..OK...
\n" ); document.write( "and
\n" ); document.write( " $\"%28%281+-+i%29+%2F+sqrt+%282%29%29%5E2+=+-i\"$ .....VERY GOOD OK....
\n" ); document.write( "The following should be true, but I can't seem to prove it
\n" ); document.write( "

\n" ); document.write( "I run into a sign problem- keep getting +1 = -1...THIS IS DUE TO THE REASON MENTIONED ABOVE..CHECK WITH THE ABOVE ADVICE AND YOU WILL AVOID THAT FALLACY OR PITFALL...OK...IF STILL IN DOUBT COME BACK...
\n" ); document.write( "Thanks for your help \n" ); document.write( "

\n" );