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Can you solve this?

 Dec 4, 2018
 #1
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\(\text{I'm not seeing anything clever}\\ \begin{array}{lr} z_1=1+i &|z_1-i| = 1\not < \dfrac 1 2\\ z_2 = \dfrac{2}{2}+i = 1+i &|z_2-i|=1 \not < \dfrac 1 2 \\ z_3 = \dfrac{2}{3}+i &|z_3-i| = \dfrac 2 3 \not < \dfrac 1 2\\ z_4 = \dfrac{13}{36}+i &|z_4-i| = \dfrac{13}{36} < \dfrac 1 2 \end{array}\\ \text{the least value of }n \text{ such that }|z_n-i|<\dfrac 1 2 \text{ is }n=4\)

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 Dec 5, 2018

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