Subjects complex numbers

Complex Rotation

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Complex Rotation


1. The problem asks us to find the complex number obtained by rotating the complex number $2+i$ by 90° anticlockwise. 2. A rotation of 90° anticlockwise in the complex plane corresponds to multiplying the complex number by $i$. 3. The original complex number is $2+i$. 4. Multiply by $i$ to rotate 90° anticlockwise: $$ (2+i) \times i = 2i + i^2 $$ 5. Recall that $i^2 = -1$, so substitute: $$ 2i + (-1) = -1 + 2i $$ 6. Therefore, after rotation, the new complex number is $-1 + 2i$. Answer: $-1 + 2i$