[Moved] the confuse about √(-1)=i and 1÷(√(-1))=-i

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weixiaodong1988

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√(-1)=i
1÷(√(-1))=-i
√(1÷(-1))=i=√(-1)÷(1))

i am confused about this :
√(1÷(-1))=i=(√(-1))÷(√1)≠(√1)÷(√(-1))=-i
i want to know why(√(1÷(-1)))≠(√1)÷(√(-1))?
 

Why do you expect (√(1÷(-1)))=(√1)÷(√(-1)) ?
(√(a÷b)=(√a)÷(√b) is true when you are dealing with real numbers.
 

Some cases that satisfy (√(a÷b)=(√a)÷(√b) don't make (√(a÷b)=(√a)÷(√b) is true for imaginary numbers. If there is even a single case that doesn't satisfy the formula, it loses generality and you cannot claim the formula is true in general.

I'm pretty sure your textbook says (√(a÷b)=(√a)÷(√b), with an annotation that a and b are real numbers.
 
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if a and b are real numbers，( √(a÷b)=(√a)÷(√b) ？ ; i think a and b must be positive numbers ( √(a÷b)=(√a)÷(√b).
i am confused about this because of the propagation constant β about LHM is a negative number.
 

My bad, yes you are right. a and b should be positive numbers to satisfy √(a÷b)=(√a)÷(√b).
 

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