Re:--Multiplication w. Complex Number Involvement

$\displaystyle (3\sqrt{-5})(-4\sqrt{-12})$

$\displaystyle (3)(i\sqrt{5}) \times (-4)(i)(\sqrt{4 \times 3})$

$\displaystyle (3i)(\sqrt{5}) \times (-4i)(2)(\sqrt{3})$

$\displaystyle (3i)(\sqrt{5}) \times (-8i)(\sqrt{3})$

$\displaystyle (-24)(i^2)(\sqrt{15})$

$\displaystyle (-24)(-1)(\sqrt{15})$

$\displaystyle 24\sqrt{15}$

$\displaystyle \sqrt{15} \approx 3.873$

$\displaystyle 24 \times 3.873 \approx 92.952$

So, $\displaystyle (3\sqrt{-5})(-4\sqrt{-12}) \approx 92.952$ . . .

Ain't that sometin!! In a million years I would never have guessed that $\displaystyle (3\sqrt{-5})(-4\sqrt{-12})$ is equal to that.

Complex numbers play "funny" tricks on old neurons! My parents should have started me on this when I was six! Maybe even three!