Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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...")
 
(→‎Problem 25)
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
==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>.
+
 
 +
==Problem 21==
 +
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 11:40, 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 $2a+b+2c+d+e$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_MECC_Mock_AMC_12&oldid=152215"