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IB Mathematics: Applications and Interpretation HL · AHL 6: Complex Numbers · AHL 6.1

The number i and Cartesian form Problem set A Answers

Skills

    1. (a) \(i\)
    2. (b) \(6i\)
    3. (c) \(-16\)
    4. (d) \(-8i\)
    1. (a) \(9i\)
    2. (b) \(4 \sqrt{3}\,i\)
    3. (c) Re = 5, Im = −4
    1. (a) \(2 + 7i\)
    2. (b) \(-5 + 9i\)
    1. (a) \(22 - 7i\)
    2. (b) \(-15\)
    1. (a) \(-45 + 28i\)
    2. (b) \(15 - 8i\)
    1. (a) \(10 - 16i\)
    2. (b) \(10 + 5i\)
    1. (a) \(17 + 28i\)
    2. (b) \(i\)
    1. (a) Dina is right: 10. Karim used \(i^2 = +1\).
    2. (b) \(4 - 4i\). No two terms are multiplied, so no \(i^2\) appears.

In context

    1. (a) \(5 - 3i\) ohms
    2. (b) \(7 - 11i\) volts

Stretch

    1. (a) 0
    2. (b) \(-1 + i\)
    1. (a) Shown
    2. (b) \(16\)

jmaths.xyz · AI HL · AHL 6.1 The number i and Cartesian form