#### burgerandcheese

##### Junior Member

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- Thread starter burgerandcheese
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If that is not enough to help, please identify what specifically you are still confused by.

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I don't understand how they got 2(cos(pi/3) + i*sin(pi/3))

If that is not enough to help, please identify what specifically you are still confused by.

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That is 2e^(pi/3 i), which is a multiplication by 2, and a rotation by pi/3 radians, which is just what they said they wanted to do.I don't understand how they got 2(cos(pi/3) + i*sin(pi/3))

If that is not clear, what

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What I know is if we have t = q(cos(β) + isin(β)) and represent it as vector AT and s = p(cos(α) + isin(α)), then w = st represented as a vector AW is rotated from AT anticlockwise by α radians or rotated from the same horizontal axis by (α + β) radians and has magnitude pq:That is 2e^(pi/3 i), which is a multiplication by 2, and a rotation by pi/3 radians, which is just what they said they wanted to do.

If that is not clear, whatdoyou know about rotation of complex numbers? We have to connect this to something you understand, and there are a couple ways you might have seen this.

This will sound weird but I don't think I know what I don't know.....

Last edited:

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So multiplying a number z by 2(cos(pi/3) + i*sin(pi/3)) will double the magnitude, and rotate by pi/3 radians (that is, add pi/3 to the angle of z). That's exactly what they want to do, right?

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I think I finally get it now. Thank you

So multiplying a number z by 2(cos(pi/3) + i*sin(pi/3)) will double the magnitude, and rotate by pi/3 radians (that is, add pi/3 to the angle of z). That's exactly what they want to do, right?

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I want to point out that AT and AW, as expressed by q*eWhat I know is if we have t = q(cos(β) + isin(β)) and represent it as vector AT and s = p(cos(α) + isin(α)), then w = st represented as a vector AW is rotated from AT anticlockwise by α radians or rotated from the same horizontal axis by (α + β) radians and has magnitude pq:

View attachment 12574

This will sound weird but I don't think I know what I don't know.....

vector