Difference between revisions of "2012 AIME II Problems/Problem 6"
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== Problem 6 == | == Problem 6 == | ||
Let <math>z=a+bi</math> be the complex number with <math>\vert z \vert = 5</math> and <math>b > 0</math> such that the distance between <math>(1+2i)z^3</math> and <math>z^5</math> is maximized, and let <math>z^4 = c+di</math>. Find <math>c+d</math>. | Let <math>z=a+bi</math> be the complex number with <math>\vert z \vert = 5</math> and <math>b > 0</math> such that the distance between <math>(1+2i)z^3</math> and <math>z^5</math> is maximized, and let <math>z^4 = c+di</math>. Find <math>c+d</math>. | ||
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+ | == Solution == | ||
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+ | == See also == | ||
+ | {{AIME box|year=2012|n=II|num-b=5|num-a=7}} |
Revision as of 16:20, 31 March 2012
Problem 6
Let be the complex number with and such that the distance between and is maximized, and let . Find .
Solution
See also
2012 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |