SOLUTION: Is the square root of plus or minus 5 (where the plus and minus are in front of the square root sign) the same thing as 5i and -5i ? If not what does 5i and -5i really mean?

Question 27616: Is the square root of plus or minus 5 (where the plus and minus are in front of the square root sign) the same thing as 5i and -5i ?
If not what does 5i and -5i really mean?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Is the square root of plus or minus 5 (where the plus and minus are in front of the square root sign) the same thing as 5i and -5i ?
YOU TRY TO UNDERSTAND AND REMEMBER THE FOLLOWING WAY
SQUARE ROOT OF ANY POSITIVE NUMBER IS SAME AS YOU KNOW ALREADY...
SAY SQRT.4= +2 OR - 2
SQRT.5 = +SQRT.5 OR -SQRT.5..
NOW COMING TO NEGATIVE NUMBERS ANY NEGATIVE NUMBER CAN BE TAKEN AS -1*THE POSITIVE NUMBER..SAY -4 = (-1)*(4)...OR...-5 = (-1)*(5) ...ETC....
SO WHEN WE WANT TO TAKE SQUARE ROOT OF NEGATIVE NUMBER WE CAN SPLIT IT INTO 2 PARTS AS ABOVE ..SQUARE ROOT OF POSITIVE PART , YOU ALREADY KNOW AS MENTIONED ABOVE.THERE IS ACTUALLY NO REAL NUMBER EXISTING WHICH IS SQUARE ROOT OF -1.SO WE IMAGINE IT IS "I"..IT IS PURELY IMAGINARY..IT DOES NOT EXIST..WE JUST TAKE IT THAT SQUARE ROOT OF -1 IS "I".HENCE SQUARE ROOT OF ANY NEGATIVE NUMBER IS
I*SQUARE ROOT OF THE POSITIVE PART THAT IS
SQUARE ROOT OF A NEGATIVE NUMBER SAY -5 =SQUARE ROOT OF (-1)*(5)
=SQUARE ROOT OF (-1)*SQUARE ROOT OF (5)=I*SQUARE ROOT OF(5)
SO
SQUARE ROOT OF (-5)= I*{SQUARE ROOT OF(5)} OR I*{-SQUARE ROOT OF(5)}
AND NOT REPEAT NOT =I*5..OR I*(-5)..
5I OR -5I IS THE SQUARE ROOT OF -25.

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