evaluate sqrt(-3)*sqrt(-12)

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- Jun 25th 2013, 09:29 AMangelamoniqueevaluating complex numbers
evaluate sqrt(-3)*sqrt(-12)

- Jun 25th 2013, 09:44 AMPlatoRe: evaluating complex numbers
In many modern treatments, we agree that $\displaystyle \sqrt{-3}$ in not defined.

However we can enlarge the number system by one symbol. We say that $\displaystyle i$ is a solution for $\displaystyle x^2+1=0$.

In effect we now have $\displaystyle i^2=-1$. Now we can say $\displaystyle \sqrt{-3}=\sqrt{3}\;i$.

So now your question becomes $\displaystyle (\sqrt{3}\;i)(\sqrt{12}\;i)=-\sqrt{36}$ - Jun 25th 2013, 09:47 AMangelamoniqueRe: evaluating complex numbers
is it 15i^2 ?

- Jun 25th 2013, 09:48 AMangelamoniqueRe: evaluating complex numbers
ohhh thanks!! :)

- Jun 25th 2013, 09:59 AMangelamoniqueRe: evaluating complex numbersQuote:
- Jun 25th 2013, 10:10 AMReneGRe: evaluating complex numbers
Aside from the arithmetic mistake, Plato was correct. Express the radicals in terms of

and simplify. $\displaystyle \sqrt{-3}\sqrt{-12} = i\sqrt{3}\,\,i\sqrt{12} = i^2\sqrt{36} = -6$ Recall that $\displaystyle i^2 = -1$*i*