Question

Complex number
√-6(2+√-8)

Answer 1

\[\Large \sqrt{-6}(2+\sqrt{-8})\]

\[\Large \sqrt{-6}*2+ \sqrt{-6}*\sqrt{-8}\]

\[\Large 2\sqrt{-6}+ \sqrt{-6}*\sqrt{-8}\]

\[\Large 2\sqrt{-1}*\sqrt{6}+ \sqrt{-1}*\sqrt{6}*\sqrt{-1}*\sqrt{8}\]

Keep going to simplify

Answer 2

There's the thing, if I could simplify I would... I got up to there and then stopped...

Answer 3

keep in mind that \[\Large i = \sqrt{-1}\]

Answer 4

\[\Large \sqrt{-6}(2+\sqrt{-8})\]

\[\Large \sqrt{-6}*2+ \sqrt{-6}*\sqrt{-8}\]

\[\Large 2\sqrt{-6}+ \sqrt{-6}*\sqrt{-8}\]

\[\Large 2\sqrt{-1}*\sqrt{6}+ \sqrt{-1}*\sqrt{6}*\sqrt{-1}*\sqrt{8}\]

\[\Large 2i*\sqrt{6}+ i*\sqrt{6}*i*\sqrt{8}\]

\[\Large 2i*\sqrt{6}+ i*i*\sqrt{6}*\sqrt{8}\]

\[\Large 2i*\sqrt{6}+ i^2*\sqrt{6*8}\]

\[\Large 2i*\sqrt{6}+ (-1)*\sqrt{48}\]

\[\Large 2i*\sqrt{6}+ (-1)*\sqrt{16*3}\]

\[\Large 2i*\sqrt{6}+ (-1)*\sqrt{16}*\sqrt{3}\]

\[\Large 2i*\sqrt{6}+ (-1)*4*\sqrt{3}\]

\[\Large 2i*\sqrt{6}-4*\sqrt{3}\]

\[\Large -4*\sqrt{3}+2i*\sqrt{6}\]

Answer 5

you can also proceed as follows
\[\sqrt{-6}=\sqrt{6}i\] and
\[\sqrt{-8}=\sqrt{8}i\] maybe that would help
then it is the distributive law recalling that when you see \(i^2\) you replace it by \(-1\)

Answer 6

Nooow I got it, lol thank you Jim.

Answer 7

You can optionally rearrange the terms to get


\[\Large -4*\sqrt{3}+2\sqrt{6} * i\]