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.


Inspiration.

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