# i cubed = real number?

Discussion in 'Math' started by strantor, Oct 7, 2012.

1. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
5,025
3,099
I'm doing online homework, and the question is
The correct answers, verified by the system, are:
${-8, 4-4\sqrt{3}i, 4+4\sqrt{3}i}$

I don't understand how the last 2 are correct, because i X i = -1, so $(4+4\sqrt{3}i ) * (4+4\sqrt{3}i )$ should be a real number, but $(4+4\sqrt{3}i ) * (4+4\sqrt{3}i ) * (4+4\sqrt{3}i )$should be an imaginary number, correct?

2. ### Papabravo Expert

Feb 24, 2006
12,272
2,721
Wrong. Multiply it out and see how the terms with the imaginary unit cancel each other out.

strantor likes this.
3. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
5,025
3,099
DOH! Yep, they sure do.
Thanks

EDIT:
I was also wrong about $(4+4\sqrt{3}i ) * (4+4\sqrt{3}i )$ being a real number.

4. ### Papabravo Expert

Feb 24, 2006
12,272
2,721
No sweat. We all have occasional lapses where our intuition plays tricks on us.

5. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
Just want to chime and say that it's good to see someone asking "does the answer make sense?", and that includes asking it of the "book's" answers, since the book will be wrong from ime to time.

strantor and Papabravo like this.