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October 20th, 2011, 09:16 AM   #1
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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]
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October 20th, 2011, 03:01 PM   #2
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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.
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October 21st, 2011, 11:27 AM   #3
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Re: 2011 complex numbers examination

That looks good!

It would be a tough 120 minutes for me, even at my finest
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October 21st, 2011, 02:29 PM   #4
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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.
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October 25th, 2011, 02:42 AM   #5
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Re: 2011 complex numbers examination

The test paper attached above has been updated and now gives correct solutions for Question 3.
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October 25th, 2011, 05:44 AM   #6
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Re: 2011 complex numbers examination

Quote:
Originally Posted by CherryPi
Part B troubles me because I have yet to take trigonometry. -_- I need to do some studying and come back to this.
The fun thing is that I never understood trig very well until I learned complex numbers, which make many of the mysterious parts of trig make sense.
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October 25th, 2011, 08:40 AM   #7
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4 a.





4 b.



4 c.

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