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I read addition and multiplication with complex numbers can be represented as translation and rotation in a 2D plane.

I am using this to move around objects on the screen. I have an offset number, that I multiply by a number representing an angle. I then use the offset to move an object in a certain direction.

To draw the actual object, I came across affine transformations, represented as a 3x3 matrix. I was wondering if I could apply these transformations directly to the matrix.

I can't say I fully understand matrix multiplication, but as far as I can tell, translation can be expressed using matrix multiplication.

So what about rotation a point around an origin?

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    Consider the matrix $\begin{pmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{pmatrix}$.2012-02-18
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    [Very related...](http://math.stackexchange.com/questions/51292)2012-02-18
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    Also: the matrix multiplication view of translation only works if you use [homogeneous coordinates](https://en.wikipedia.org/wiki/Transformation_matrix). Otherwise, you can only translate by adding an appropriate vector to your original vector.2012-02-18

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