Why is sin(-π/2)^(1/2) undefined? sin(-π/2) is -1, so I thought the the answer would be the same, -1^(1/2)=-1? But my calculator and the answers sheet both say undefined...
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$\begingroup$Why do you think the principal square root of $-1$ is $-1$? That would suggest that $(-1)^2=(-1)\times(-1)=-1$ when clearly $(-1)\times(-1)=+1$. Instead, we have $(-1)^\frac12=i$ -- have you learned about imaginary numbers yet?
$\endgroup$ $\begingroup$The square root of a number $a$ is a number $b$ such that $$b\cdot b=a$$
Since a positive number times a positive number is also a positive number,
and a negative number times a negative number is a positive number,
we get that there is no (real) number that can be multiplied by itself to get a negative number.
That is: Negative numbers does not have a (real) square root.
$\endgroup$ $\begingroup$I think whether question or problem is right is depend on the field or number field you choose. More accurately, if you talk this in $R$, then $i$ is not defined. However, $i$ is defined in $C$.
$\endgroup$ $\begingroup$What everyone else is saying is -1^(1/2) is undefined, because anything ^(1/2) means it's the square root. (AKA x^(1/2) = sqrt(x)). (-pi/2) is negative so trying to get a square root of it doesn't work, and is therefore undefined.
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