Difference between revisions of "2011 AMC 12A Problems/Problem 23"
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== Problem == | == Problem == | ||
| + | Let <math>f(z)= \frac{z+a}{z+b}</math> and <math>g(z)=f(f(z))</math>, where <math>a</math> and <math>b</math> are complex numbers. Suppose that <math>\left| a \right| = 1</math> and <math>g(g(z))=z</math> for all <math>z</math> for which <math>g(g(z))</math> is defined. What is the difference between the largest and smallest possible values of <math>\left| b \right|</math>? | ||
| + | |||
| + | <math> | ||
| + | \textbf{(A)}\ 0 \qquad | ||
| + | \textbf{(B)}\ \sqrt{2}1 \qquad | ||
| + | \textbf{(C)}\ \sqrt{3}-1 \qquad | ||
| + | \textbf{(D)}\ 1 \qquad | ||
| + | \textbf{(E)}\ 2 </math> | ||
| + | |||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
{{AMC12 box|year=2011|num-b=22|num-a=24|ab=A}} | {{AMC12 box|year=2011|num-b=22|num-a=24|ab=A}} | ||
Revision as of 02:37, 10 February 2011
Problem
Let 
and 
, where 
and 
are complex numbers. Suppose that 
and 
for all 
for which 
is defined. What is the difference between the largest and smallest possible values of 
?
Solution
See also
| 2011 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 22 |
Followed by Problem 24 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
