Complex Number transformations Watch

Cataclysm
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#1
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Guys, I need a bit of help with complex number graphing and transformations.

Suppose you have a point A with and in form a+bi it is -3+5i. Now let's say you have point B which is a 'transformation' of A and is in the form 5+3i. What has been the transformation.

So far I have figured out that to get from -3+5i to 5+3i you have to multiply A by -i.

Is that sufficient. A transformation by -i? Or do you need to talk about angles. I'm just interested in noting how the exact translation is described because the points do seem to have one about the origin (?)

BTW, I am new to complex transformations and never did Further Maths so I don't understand all the concepts so I would prefer a simplified or a well-explained answer. Thanks!
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Cataclysm
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Also, do you guys know any good sites to learn about complex numbers online if you have sufficient A-level Maths knowledge?
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thomaskurian89
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(Original post by Cataclysm)
So far I have figured out that to get from -3+5i to 5+3i you have to multiply A by -i.

Is that sufficient. A transformation by -i? Or do you need to talk about angles. I'm just interested in noting how the exact translation is described because the points do seem to have one about the origin (?)
Yes, it is sufficient! Note that when you multiply a complex number by -i, the point shifts clockwise by 90 degrees but the magnitude (distance from the origin) remains the same.
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Cataclysm
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(Original post by thomaskurian89)
Yes, it is sufficient! Note that when you multiply a complex number by -i, the point shifts clockwise by 90 degrees but the magnitude (distance from the origin) remains the same.
Thanks! I thought it looked like a right angle transformation as well in my sketch! Thanks mate.
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Kolya
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I think it is most common to talk about transformations in terms of matrices, but if that idea makes no sense yet then what you have written is fine. (It's fine anyway, but just less common.)
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thomaskurian89
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(Original post by Cataclysm)
Thanks! I thought it looked like a right angle transformation as well in my sketch! Thanks mate.
you're welcome!
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SimonM
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Bear in mind that this could also be a simple translation as well
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