SOLUTION: I am trying to find out if these are true: {{{(1 + i) / sqrt (2) = sqrt (i)}}} and {{{(1 - i) / sqrt (2) = sqrt (-i)}}} I can verify {{{((1 + i) / sqrt (2))^2 = i}}} and {{

Question 27172: I am trying to find out if these are true:

and

I can verify

and

The following should be true, but I can't seem to prove it

I run into a sign problem- keep getting +1 = -1
Thanks for your help
Answer by venugopalramana(3286) (Show Source): 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.
THE PROBLEM ARISES WHEN ONE TRIES TO COMBINE RULES FOR REAL NUMBERS WITH THOSE FOR COMPLEX NUMBERS.TO SUM UP
*= 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
LET US DO WITH AN EXAMPLE PUTTING NUMBERS FOR a AND b.
*= IS NOT CORRECT AS BOTH NUMBERS ARE NEGATIVE..IT LEADS TO ABSURD RESULT OF
LHS=2i*3i=6i^2=-6.....RHS=+6...THAT IS -6=+6....ABSURD
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......
HOPE IT IS CLEAR..NOW YOU CAN EASILY SEE WHERE YOU HAVE DONE CORRECTLY AND WHERE YOU ERRED....
I am trying to find out if these are true:

and

I can verify
....VERY GOOD ..OK...
and
.....VERY GOOD OK....
The following should be true, but I can't seem to prove it

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...
Thanks for your help
RELATED QUESTIONS
Can someone help me with this i've tried and i am not ending up with the right solutions. (answered by tutorcecilia)

{{{ (1/2 + (sqrt(3)/2) i )^2... (answered by Edwin McCravy)

How can i rationalise this surd {{{ 1/(sqrt(2)+sqrt(3)+sqrt(5)) }}} (answered by ikleyn)

can i multiply sqrt of 6 and sqrt of... (answered by Fombitz)

How will I go about simplifing these problem? 1) 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] (answered by edjones)

I need to find the answer to the sqrt of -8 ( sqrt -3 - sqrt 5) ugh. I got i sqrt 8 (i... (answered by addingup,MathTherapy)

{{{ (2-i)/ (sqrt(3) - i)... (answered by robertb)

i need some help with these i am trying to solve these by quadratic equation formula and... (answered by MathLover1)

How can i find a common difference for this arithmetic sequence? {{{ 1/sqrt (2) }}},{{{ (answered by Theo)