The Argand diagram — A/L Combined Mathematics

How do I practise The Argand diagram?

1 question with a worked solution

Check before you answer: Principal Argument Determination: Correctly quadrant-adjusting θ = Arg(z) within the strict statutory interval (-π, π] (e.g., Arg(-1 - i) = -3π/4, not 5π/4).

1. On an Argand diagram, multiplying a complex number z by the imaginary unit i represents which geometric transformation of the vector representing z?
   1. A) A clockwise rotation by 90° about the origin
   2. B) A doubling of the vector length along its original line
   3. C) An anticlockwise rotation by 90° (π/2 radians) about the origin without changing magnitude
   4. D) A reflection across the real horizontal axis
   Check my answer

   Correct answer: C) An anticlockwise rotation by 90° (π/2 radians) about the origin without changing magnitude

   In polar/exponential form, i = cos(π/2) + i sin(π/2) = e^iπ/2. Multiplying z = r e^iθ by i yields z · i = r e^{i(θ + π/2)}, which rotates the position vector anticlockwise by π/2 (90°) about the origin with its modulus r unchanged.

   Show worked solution

   Step 1: Write i in polar form: i = 1 · (cos 90° + i sin 90°). Step 2: Argument increases by +90° while modulus is multiplied by 1. Answer: An anticlockwise rotation by 90° (π/2 radians) about the origin without changing magnitude.
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does The Argand diagram fit in the syllabus?

Year 2 · Term 1