Compleksh for u

If the complex sequence of numbers z₀, z₁, z₂........satisfy z_0=i+\frac{1}{137} and for nâ‰¥1 z_{n+1}=\frac{z_n+i}{z_n-i}

then find the value of z₂₀₀₇

2 Answers

341

Hari Shankar ·2010-09-04 02:02:41

Let z_n = ix_n

Then the sequence satisfies x_{n+1} = \frac{x_n+1}{x_n-1} which is easy to see satisfies x_{n+2} = x_n

From this it is easy to see that z₂₀₀₇=z₁ which can be easily computed

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