Question

Simplify the complex expression and show work

Answer 1

The answer is

$(-9+3\sqrt{2})+(3\sqrt{2}-2)i$

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Work Shown:

$(-3+\sqrt{-2})(3-\sqrt{2})$

$(-3+\sqrt{-1*2})(3-\sqrt{2})$

$(-3+\sqrt{-1}*\sqrt{2})(3-\sqrt{2})$

$(-3+i\sqrt{2})(3-\sqrt{2})$

$x(3-\sqrt{2})$ let $x=-3+i\sqrt{2}$

$3x-x*\sqrt{2}$ distribute

$3(x)-\sqrt{2}(x)$

$3(-3+i\sqrt{2})-\sqrt{2}(-3+i\sqrt{2})$

$-9+3i\sqrt{2}+3\sqrt{2}-i*\sqrt{2}*\sqrt{2}$

$-9+3i\sqrt{2}+3\sqrt{2}-2i$

$-9+3\sqrt{2}+3i\sqrt{2}-2i$

$(-9+3\sqrt{2})+(3\sqrt{2}-2)i$

The use of parenthesis in the last step is to help separate out the terms.

The last expression shown above is in the form a+bi where

$a=-9+3\sqrt{2}$

$b=3\sqrt{2}-2$