A 2D vector (x, y) can be represented by the complex number z = x + iy. To rotate this vector by an angle θ, it is multiplied by the complex number e^(iθ) = cos(θ) + i sin(θ). If the vector (3, 4) is rotated by 90 degrees (π/2 radians) using this method, what are the coordinates of the new, rotated vector?
0
1
Tags
Ch.2 Generative Models - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
Application in Bloom's Taxonomy
Cognitive Psychology
Psychology
Social Science
Empirical Science
Science
Related
Formula for Applying RoPE Rotation 't' Times
Definition of C(x, tθ) Notation for Rotated Tokens
Component-wise Vector Rotation in Complex Space
A 2D vector (x, y) can be represented by the complex number z = x + iy. To rotate this vector by an angle θ, it is multiplied by the complex number e^(iθ) = cos(θ) + i sin(θ). If the vector (3, 4) is rotated by 90 degrees (π/2 radians) using this method, what are the coordinates of the new, rotated vector?
A 2D vector can be rotated by representing it as a complex number and multiplying it by another complex number that represents the rotation. Arrange the following steps in the correct logical order to derive the coordinates of a vector
(x₁, x₂)after it has been rotated by an angleθ.Mapping Complex Multiplication to Rotated Vector Components