complex numbers: (6sqrt[2] + i)(-3 + isqrt[2])

G

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I have this question that i cant get right: Multiply these complex numbers
(6√2 + i)X(-3 + i√2)

that √ means square root

I have -18√2 + 7√2i - 3i + √2i^2
-18√2 + (7√2 - 3)i - √2
-19√2 + (7√2 - 3)i
but the answer is -19√2 + 9i
what am i doing wrong? :(

Thank you for your time [/list][/code]
 
\(\displaystyle \L (6\sqrt{2} + i)(-3 + i\sqrt{2})\)

\(\displaystyle \L 6\sqrt{2}(-3 + i\sqrt{2}) + i(-3 + i\sqrt{2})\)

\(\displaystyle \L -18\sqrt{2} + 12i - 3i + i^2\sqrt{2}\)

\(\displaystyle \L -18\sqrt{2} + 12i - 3i -\sqrt{2}\)

\(\displaystyle \L -19\sqrt{2} + 9i\)
 
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