Question

Simplify the complex expression and show work

Answer 1

The answer is

`(-9+3√(2))+(3√(2)-2)i`

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Work Shown:

`(-3+√(-2))(3-√(2))`

`(-3+√(-1*2))(3-√(2))`

`(-3+√(-1)*√(2))(3-√(2))`

`(-3+i√(2))(3-√(2))`

`x(3-√(2))` let
`x=-3+i√(2)`

`3x-x*√(2)` distribute

`3(x)-√(2)(x)`

`3(-3+i√(2))-√(2)(-3+i√(2))`

`-9+3i√(2)+3√(2)-i*√(2)*√(2)`

`-9+3i√(2)+3√(2)-2i`

`-9+3√(2)+3i√(2)-2i`

`(-9+3√(2))+(3√(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√(2)`

`b=3√(2)-2`