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PostPosted: Thu, 10 May 2012 15:40:59 UTC 
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Let z = re^{i\Theta} and w = ke^{i\alpha}

Let P be the point that corresponds to z.

The point Q that corresponds to the complex number zw is obtained by
1) scaling of the distance OP by the factor k, followed by,
2) rotating the point P anticlockwise about the origin through the angle \alpha

If k < 0, then scaling of distance from the origin by a factor of |k| will be in the opposite direction.

My issue: this is from some notes I have from school and I don't understand the last sentence. What does it mean, "scaling of distance will be in the opposite direction"?

thank you!


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PostPosted: Thu, 10 May 2012 19:23:51 UTC 
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thesocialnetwork wrote:
Let z = re^{i\Theta} and w = ke^{i\alpha}

Let P be the point that corresponds to z.

The point Q that corresponds to the complex number zw is obtained by
1) scaling of the distance OP by the factor k, followed by,
2) rotating the point P anticlockwise about the origin through the angle \alpha

If k < 0, then scaling of distance from the origin by a factor of |k| will be in the opposite direction.

My issue: this is from some notes I have from school and I don't understand the last sentence. What does it mean, "scaling of distance will be in the opposite direction"?

thank you!


If k<0 then write k=-|k| then use that -1=e^{i\pi} and you get your original case with |k|e^{i(\alpha+\pi)} which, of course, means you scale by |k| and the \pi bit of the angle forces you another 180 degree rotation, which is in the opposite direction of the original.

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