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Rotations on an Argand diagram

The point AA represents a fixed complex number aa where π/4<arg⁡(a)<π/2\pi/4<\arg(a)<\pi/2. The complex numbers −ia-ia and −a-a are represented by the points BB and CC respectively.

On a single clearly labelled Argand diagram, mark the points AA, BB and CC.

Describe the geometrical relationship between

(a) AA and BB, and

(b) AA and CC.

[2023/TJC_NYJC_VJC/FM/I/6(modified)]

CJC · Discussion · Question 9

Multiplying by −i changes the argument by −π/2 and leaves the modulus unchanged.

Read the worked solution