Multiplying a non-zero complex number by \( \frac{1 - i}{1 + i} \) results in a rotation about the origin on an Argand diagram - HSC - SSCE Mathematics Extension 2 - Question 5 - 2016 - Paper 1

The complex number ( -i ) can be represented in polar form. Each complex number can be written as ( re^{i\theta} ), where ( r ) is the modulus and ( \theta ) is the argument. Here, the modulus is 1 and the argument corresponds to the angle of a rotation:

• The angle ( \theta = \frac{3\pi}{2} ) radians, which corresponds to a rotation of ( \frac{\pi}{2} ) radians in the clockwise direction.

Thus, multiplying by ( \frac{1 - i}{1 + i} ) results in a clockwise rotation by ( \frac{\pi}{2} ), leading to the answer (B).