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True or False?
(1+i)(−1+i)(−1−i)(1−i)=14(1+3i)(−1+3i)(−1−3i)(1−3i) ( 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 ) (1+i)(−1+i)(−1−i)(1−i)=41(1+3i)(−1+3i)(−1−3i)(1−3i)
Clarification: i=−1i=\sqrt{-1}i=−1.
Bonus: Prove it without expanding all the terms.
Inspiration.
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