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Difference between revisions of "2021 MECC Mock AMC 12"

(Created page with "==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</m...")
 
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==Problem 25==
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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>.
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==Problem 21==
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The exact value of <math>\sqrt{\sqrt{\sqrt{\sqrt{\frac{-1-\sqrt{3}i}{2}}}}}</math> can be expressed as <math>\frac{\sqrt{a}+\sqrt{b}+i\sqrt{c}-i\sqrt{d}}{e}</math> which the fraction is in the most simplified form and <math>a</math>, <math>b</math>, <math>c</math>, <math>d</math> and <math>e</math> are not necessary distinct positive integers. Find <math>2a+b+2c+d+e</math>

Latest revision as of 10:40, 21 April 2021


Problem 21

The exact value of $\sqrt{\sqrt{\sqrt{\sqrt{\frac{-1-\sqrt{3}i}{2}}}}}$ can be expressed as $\frac{\sqrt{a}+\sqrt{b}+i\sqrt{c}-i\sqrt{d}}{e}$ which the fraction is in the most simplified form and $a$, $b$, $c$, $d$ and $e$ are not necessary distinct positive integers. Find $2a+b+2c+d+e$

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