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Complex numbers help 
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#1
Jul614, 08:02 AM

P: 12

We know that i^3 is i .
But I am getting confused, because I thought that i can be written as √(1) and i^3 = √(1) × √(1) × √(1) = √(1 × 1 × 1) = √( (1)^2 × 1) = √(1× 1) = √(1) = i ( and not i ). Please help. Sorry I couldn't use superscript because I was using my phone. 


#2
Jul614, 09:01 AM

Mentor
P: 18,019



#3
Jul614, 10:22 AM

P: 1

i definitely is not \sqrt{1}. If you like (abuse of notation)
\sqrt{1} = \pm i Using (this not correct notation) \sqrt{1}^3 = \pm i. Much better is of course i^3 = (i*i)*i = 1*i = i 


#4
Jul614, 10:38 AM

P: 12

Complex numbers help



#5
Jul614, 10:39 AM

P: 12




#6
Jul714, 09:25 AM

P: 7

The link given by micromass has everything you need to know and you don't need to know Euler's Formula to understand what he meant. I suggest read (not skim) the link provided by micromass. 


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