Avoid Doing Complex Arithmetic

Algebra Level 3

True or False?

\[ ( 1 + i)( 1 + 2i) ( 1+3i) = ( 1 - i ) ( 1 - 2i) ( 1-3i) \]

\[\] Clarification: \(i=\sqrt{-1}\).

Bonus: Prove it without expanding all the terms.

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