Difference between revisions of "1992 AHSME Problems/Problem 15"

(Created page with "== Problem == Let <math>I=\sqrt{-1}</math>. Define a sequence of complex numbers by <cmath>z_1=0,\quad z_{n+1}=z_{n}^2+i \text{ for } n\ge1.</cmath> In the complex plane, how f...")
 
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== Problem ==
 
== Problem ==
  
Let <math>I=\sqrt{-1}</math>. Define a sequence of complex numbers by
+
Let <math>i=\sqrt{-1}</math>. Define a sequence of complex numbers by
  
 
<cmath>z_1=0,\quad z_{n+1}=z_{n}^2+i \text{ for } n\ge1.</cmath>
 
<cmath>z_1=0,\quad z_{n+1}=z_{n}^2+i \text{ for } n\ge1.</cmath>
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== Solution ==
 
== Solution ==
<math>\fbox{A}</math>
+
<math>\fbox{B}</math>
  
 
== See also ==
 
== See also ==

Revision as of 15:09, 28 September 2014

Problem

Let $i=\sqrt{-1}$. Define a sequence of complex numbers by

\[z_1=0,\quad z_{n+1}=z_{n}^2+i \text{ for } n\ge1.\] In the complex plane, how far from the origin is $z_{111}$?

$\text{(A) } 1\quad \text{(B) } \sqrt{2}\quad \text{(C) } \sqrt{3}\quad \text{(D) } \sqrt{110}\quad \text{(E) } \sqrt{2^{55}}$

Solution

$\fbox{B}$

See also

1992 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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