# 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