Saturday, October 1, 2011

Basic imaginary numbers from definition

i^0  = 1
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1


i^5  = i
i^6 = -1
i^7 = -i
i^8 = 1
i^9 = i

e.g.
So, i^ 325 = ?
325/4 = 8 remainder 1
( note 1 is the modulus)
same as i^1 = i

Remember, i = sqrt( -1 )

OK, a little bit More
I should really quickly note the definition:

We know that, 
i = sqrt -1
and therefore
i^2 = -1


therefore,
i^1 = i    [ anything to the power of 1 is itself ]
i^2 = -1   [ given above ]
i^3 = i^2.i^1 = -1.i = -i   
i^4 = i^3.i^2.i^1 = -i.-1.i = 1




A bit more on complex numbers

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