I keep getting “The imaginary unit” questions wrong in Complex Numbers. What's the trap?
writing √(−1)·√(−1) = √1 = 1.
The usual trap: writing √(−1)·√(−1) = √1 = 1. How to avoid it: the rule √a·√b=√(ab) fails for negatives — i² = −1, not +1. Go back to the definition — i is defined by i² = −1, letting us handle square roots of negative numbers.
Key point
The imaginary unit
Common mistake
writing √(−1)·√(−1) = √1 = 1.
Memory tip
the rule √a·√b=√(ab) fails for negatives — i² = −1, not +1.
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