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

[weixiaodong1988]

√(-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))?

 

[lostinxlation]

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

 

[weixiaodong1988]

if a and b are imaginary number (√(a÷b)=?and(√a)÷(√b) =?what is the relation about those two results?

 

[lostinxlation]

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.

 

[weixiaodong1988]

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.

 

[lostinxlation]

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

 

[weixiaodong1988]

Thank you very much .:smile: