Question

[radical -2] -3
simplify using imaginary unit i

Answer 1

By definition, \[\Large i = \sqrt{-1}\]

Answer 2

We'll use the rule

\[\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]

to simplify

Answer 3

use the rule and definition above to get...


\[\Large \sqrt{-2} - 3\]


\[\Large \sqrt{-1*2} - 3\]


\[\Large \sqrt{-1}*\sqrt{2} - 3\]


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


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


The last expression is in the form a+bi form where \(\Large a = -3\) and \(\Large b = \sqrt{2}\)