# evaluating complex numbers

• Jun 25th 2013, 09:29 AM
angelamonique
evaluating complex numbers
evaluate sqrt(-3)*sqrt(-12)
• Jun 25th 2013, 09:44 AM
Plato
Re: evaluating complex numbers
Quote:

Originally Posted by angelamonique
evaluate sqrt(-3)*sqrt(-12)

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 AM
angelamonique
Re: evaluating complex numbers
is it 15i^2 ?
• Jun 25th 2013, 09:48 AM
angelamonique
Re: evaluating complex numbers
ohhh thanks!! :)
• Jun 25th 2013, 09:59 AM
angelamonique
Re: evaluating complex numbers
Quote:
wait, i get the i-part but i don't see how you got 24. isn't sqrt(3)*sqrt(12) = sqrt(3*12) ?
• Jun 25th 2013, 10:10 AM
ReneG
Re: evaluating complex numbers
Aside from the arithmetic mistake, Plato was correct. Express the radicals in terms of i and simplify. $\displaystyle \sqrt{-3}\sqrt{-12} = i\sqrt{3}\,\,i\sqrt{12} = i^2\sqrt{36} = -6$ Recall that $\displaystyle i^2 = -1$