Difference between revisions of "2021 MECC Mock AMC 12"
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| + | ==Problem 25== | ||
| + | 25. All the solution of <math>(z-2-\sqrt{2})^{24}=4096</math> are vertices of a polygon. The smallest solution that when express in polar form, has a <math>y</math> value greater than <math>0</math> but smaller than <math>\frac{\pi}{2}</math> can be expressed as <math>\frac{\sqrt{a}+\sqrt{b}+i\sqrt{c}-i\sqrt{d}+\sqrt{e}+f+i\sqrt{g}-hi}{j}</math> which <math>a,b,c,d,e,f,g,h,j</math> are all not necessarily distinct positive integers, <math>i</math> in this case represents the imagenary number, <math>i</math>, and the fraction is in the most simplified form. Find <math>a+b+c+d+e+f+g+h+j</math>. | ||
Revision as of 11:39, 21 April 2021
Problem 25
25. All the solution of 
are vertices of a polygon. The smallest solution that when express in polar form, has a 
value greater than 
but smaller than 
can be expressed as 
which 
are all not necessarily distinct positive integers, 
in this case represents the imagenary number, , and the fraction is in the most simplified form. Find 
.
