Complex Numbers
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In an argand diagram, the point A represents the complex number 2-3^0.5+i. If A, B, C are the vertices of an equilateral triangle taken in clockwise order, and these points lie on a circle with the center at the origin, find the complex number represented by B in the form p + iq giving the exact values of p and q i know that angle of B is 120 more than the angle of A and it is of the same length. But if i calculate the angle of A and sub the values to find B, i cant get the exact value. The answer writes b=e^(-2/3pie) x (2-3^0.5 + i) b= 3^0.5 - 1 + i(1-3^0.5) I dont understand the method used in the answer. Does anyone know? Or is there another method?
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Hi,
This question is from RI(JC) 2010 paper.
To obtain B from A via a clockwise rotation of (2/3)pi about the origin, we multiply e^(-(2/3)pi*i) to the complex number represented by A.
I believe students are more familiar with the relationship between iz and z, where iz is obtained from z via an anticlockwise rotation of pi/2 about the origin. In fact, iz is equivalent to z multiplied by e^((pi/2)*i).
Thanks.
Cheers,
Wen Shih -
oh i see. thanks
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oh god...i'm so not looking forward to JC...
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Hi,
Complex Numbers is a topic taught at JC 2 and it is a difficult topic for most students.
In JC 1, the challenges are:
1. General Paper
2. Project Work
3. Fast-paced lectures and tutorials
4. Frequent class and lecture tests, typically with no time to complete.
However, one can pick up great life-skills (i.e., reading, writing and communication skills, ability to embrace an ever-changing, ever-challenging globalised economy and workplace where short deadlines to deliver results are a norm, etc.) from these.
Thanks.
Cheers,
Wen Shih -
Well, they're called complex numbers for a reason.
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To TS, u are Daniel798 huh? Because something identical was posted here:
http://forums.sgclub.com/singapore/complex_numbers_374428.html