# Rotations by degrees other than 90, 180, and 270

Say I have a triangle with vertices (0,0), (2,4), (4,0) that I want to rotate along the origin. Rotation by multiples of 90 is simple. However, I want to rotate by something a bit more complicated, such as 54 degrees. How do I figure out where the vertices would be then?

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One way is to use complex numbers. Multiplying by $\cos\theta+i\sin\theta$ rotates by $\theta$ about 0, so you could multiply $(2+4i)(\cos 54^\circ+i\sin 54^\circ)$ to get the rotation image of (2,4).