Ok if I enter (-sqrt(3))^2) into my calculator I get the answer 3. Where does the - go?
I know this is basic but...
I did that. And it preserved the negative sign.
But in my case I need to calculate a length of the vector and I know that one one of the short sides is -sqrt(3) (it is actually with complex numbers but I like to think of complex numbers at kind of vectors. Is that wrong?)
And I am using the c=sqrt(a^2+b^2).
Sin this case using -((sqrt(3)^2) is incorrect isn't it?
Ok, i will start from scratch.
I have this problem:
Write -sqrt(3)+i in polar from. (Again translated so might be the way it is normally phrased).
What i did was trying to find the |v| value:
sqrt((-sqrt(3))^2+1^2)
Now, at the (-sqrt(3))^2 is where my question comes in.
because my calculator shows that both $\displaystyle (-\sqrt{3})^2=3$ and $\displaystyle (\sqrt{3})^2=3$
Am i correct in assuming that in reality $\displaystyle (-\sqrt{3})^2=+3 or 3$?
Are then the negative value not used because it will result in a negative magnitude and that is not allowed?
Are there cases where using the pythagorean theorem in this way will result in two possible solutions for the magnitude?
You enter sqrt(3) and the calculator says 1.732...
Then make it negative and you have -1.732..
Then square that: -1.732 x -1.732 = +3.
So yes, it's a positive result. You're basically asking why a negative times a negative is a positive. And note that if your calculator had given you the negative value of sqrt(3) you'd still get the same thing: -(-1.732) x -(-1.732) = 3.