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>.
 
  
 
== Solution ==
 
== Solution ==
 
+
{{solution}}
== See also ==
+
== See Also ==
 
{{AIME box|year=2012|n=II|num-b=5|num-a=7}}
 
{{AIME box|year=2012|n=II|num-b=5|num-a=7}}

Revision as of 14:44, 3 April 2012

Problem 6

Let $z=a+bi$ be the complex number with $\vert z \vert = 5$ and $b > 0$ such that the distance between $(1+2i)z^3$ and $z^5$ is maximized, and let $z^4 = c+di$. Find $c+d$.

Solution

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See Also

2012 AIME II (ProblemsAnswer KeyResources)
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
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