Is #+-5i# the square root of #-25# ?
1 Answer
Yes and no.
Explanation:
The notation:
#+-5i#
is shorthand for the two values:
#5i" "# and#" "-5i#
So we can say that the polynomial:
#x^2+25 = 0#
has roots:
#x = +-5i#
meaning that it has roots:
#x = 5i" "# and#" "x = -5i#
In other words,
By common definition and convention, the symbols
Remarks
The
For example, we might write:
#(a+-b)^2 = a^2+-2ab+b^2#
which is true, provided that the chosen signs match.
Then again, we might say that the roots of:
#x^4-10x^2+1 = 0#
are:
#x = +-sqrt(2)+-sqrt(3)#
but in that case we would intend all