Sean M. answered • 04/26/20
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PhD Student in Mathematics
We can rewrite (1+i)/(1-i) as follows:
First, multiply the numerator and denominator by the complex conjugate (1+i). This yields:
(1+i)(1+i)/(1-i)(1+i)
=(1+i+i+i2)/(1+i-i-i2) Expanding the term
=(1+2i+(-1))/(1-(-1)) Simplifying by combining like terms and substituting i2=-1
=(2i)/(2) Again, combining like terms
=i
So we can now consider in, which is much easier to make sense of. Since i2=-1, i4 is the first term that is equal to 1. Therefore n=4.
Sean M.
I assumed n was given to be a positive integer. If asked for the "smallest possible value for n" without that constraint, there is no solution. As your logic suggests, we would keep reducing by 4 (-4, -8, -12, etc.) and we will never reach the end of this infinite sequence to come up with a "smallest" number.
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04/28/20
Ashley P.
Since they're asking for the smallest possible integer for n, we can also take minus multiples of 4 too right? That is i^(-4) etc. also would do right? So can n=4 be the smallest? How do we figure out the smallest possible integer for n Then?04/26/20