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October 20th, 2011, 09:16 AM  #1 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  2011 complex numbers examination [color=#000000]This is a test I put, for the third high school class. [attachment=1:3klpwlsq]2011comptest.pdf[/attachment:3klpwlsq] [/color] 
October 20th, 2011, 03:01 PM  #2 
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: 2011 complex numbers examination
Ah.. Beautiful. I thank you, good man. I shall give it my best shot. Understandably, I am likely to fail. 
October 21st, 2011, 11:27 AM  #3 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: 2011 complex numbers examination
That looks good! It would be a tough 120 minutes for me, even at my finest 
October 21st, 2011, 02:29 PM  #4 
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: 2011 complex numbers examination
Surprisingly, these aren't as bad as I thought. I've worked through question 1 and the majority of 2. Here are my solutions: Question 1: A. i. ii. B (I went ahead and proved these 1. T: 2. F: 3. T: 4. F: i.e. The value of z is its distance from the origin, which is derived through pythagorean theorem (or, equivalently, distance formula). 5. I don't know how to do this as I've never looked at trig seriously (just a freshman [first year] in highschool right now). Question 2: A. To answer this, I proved that is a complex number in the form with . The proof is as follows: i. ii. See above. Part B troubles me because I have yet to take trigonometry. _ I need to do some studying and come back to this. 
October 25th, 2011, 02:42 AM  #5 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: 2011 complex numbers examination
The test paper attached above has been updated and now gives correct solutions for Question 3.

October 25th, 2011, 05:44 AM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: 2011 complex numbers examination Quote:
 
October 25th, 2011, 08:40 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,474 Thanks: 2039 
4 a. 4 b. 4 c. 

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