How Complex Is It?
Algebra
Level
3
True or False?
\[ ( 1 + i)( -1 + i) ( -1-i) (1-i) = \frac{1}{4}( 1 + \sqrt{3}i ) (-1 + \sqrt{3}i ) (-1 - \sqrt{3}i )(1 - \sqrt{3}i ) \]
Clarification: \(i=\sqrt{-1}\).
Bonus: Prove it without expanding all the terms.
by
Steven Chase