Question

If the complex number \( 2 + i \) is rotated through an angle \( 90^\circ \) in the anti-clockwise direction about the origin in the complex plane, then the resulting complex number is

• A. \( 2 - i \)
• B. \( 1 + 2i \)
• C. \( -1 + 2i \)
• D. \( -2 + i \)
• E. \( 1 - 2i \)

Hint:

To rotate a complex number counterclockwise by \( 90^\circ \), multiply it by \( i \).

Answer 1

The Correct Option is C

A rotation by \( 90^\circ \) counterclockwise of a complex number \( z = x + iy \) can be achieved by multiplying it by \( i \), i.e., the new number is \( iz \). 
So, \[ z = 2 + i \] \[ iz = i(2 + i) = 2i - 1 = -1 + 2i \] Thus, the correct answer is (C).