Thread: evaluating complex numbers

1. evaluating complex numbers

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

2. Re: evaluating complex numbers

Originally Posted by angelamonique
evaluate sqrt(-3)*sqrt(-12)
In many modern treatments, we agree that $\sqrt{-3}$ in not defined.
However we can enlarge the number system by one symbol. We say that $i$ is a solution for $x^2+1=0$.
In effect we now have $i^2=-1$. Now we can say $\sqrt{-3}=\sqrt{3}\;i$.

So now your question becomes $(\sqrt{3}\;i)(\sqrt{12}\;i)=-\sqrt{36}$

3. Re: evaluating complex numbers

is it 15i^2 ?

4. Re: evaluating complex numbers

ohhh thanks!!

5. Re: evaluating complex numbers

So now your question becomes $(\sqrt{3}\;i)(\sqrt{12}\;i)=-\sqrt{24}$
wait, i get the i-part but i don't see how you got 24. isn't sqrt(3)*sqrt(12) = sqrt(3*12) ?

6. Re: evaluating complex numbers

Aside from the arithmetic mistake, Plato was correct. Express the radicals in terms of i and simplify. $\sqrt{-3}\sqrt{-12} = i\sqrt{3}\,\,i\sqrt{12} = i^2\sqrt{36} = -6$ Recall that $i^2 = -1$