Mathematics

Rotating a complex number in the plane is equivalent to multiplying it by another complex number on the unit circle. The key insight is that rotating by angle $\theta$ means multiplying by $e^{i\theta} = \cos\theta + i\sin\theta$. Here you'll multiply $2 + i$ by $e^{i\pi/3}$ to capture the anticlockwise rotation, then expand and simplify to find your new complex number.

Rotating a complex number in the plane is equivalent to multiplying it by another complex number on the unit circle. The key insight is that rotating by angle $\theta$ means multiplying by $e^{i\theta} = \cos\theta + i\sin\theta$. Here you'll multiply $2 + i$ by $e^{i\pi/3}$ to capture the anticlockwise rotation, then expand and simplify to find your new complex number.