Question

What's the formula for rotating a shape at 45 degrees clockwise?

Answer 1

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This can also be achieved nicely with complex numbers, using the fact that in multiplying complex numbers you multiply the lengths and add the angles. This means that to rotate a complex number zzby an angle θθ about the origin you take z⋅(cosθ+isinθ)z⋅(cos⁡θ+isin⁡θ)

To rotate zz by an angle θθ about ww, you would do (z−w)⋅(cosθ+isinθ)+w(z−w)⋅(cos⁡θ+isin⁡θ)+w. (The subtracting and adding  to and from the origin.)

example: [(2+i)−(2+2i)]⋅(−2√2+i2√2)+(2+2i)

Answer 2

Answer:

This can also be achieved nicely with complex numbers, using the fact that in multiplying complex numbers you multiply the lengths and add the angles. This means that to rotate a complex number zzby an angle θθ about the origin you take z⋅(cosθ+isinθ)z⋅(cos⁡θ+isin⁡θ)

To rotate zz by an angle θθ about ww, you would do (z−w)⋅(cosθ+isinθ)+w(z−w)⋅(cos⁡θ+isin⁡θ)+w. (The subtracting and adding  to and from the origin.)

example: [(2+i)−(2+2i)]⋅(−2√2+i2√2)+(2+2i)