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IB Mathematics: Applications and Interpretation HL · AHL 6: Complex Numbers · AHL 6.3

The complex plane and the modulus Problem set A Answers

Skills

    1. (a) \(-z = -5 - 2i\)
    2. (b) \(z^* = 5 - 2i\)
    3. (c) \(-z^* = -5 + 2i\): reflection in the imaginary axis
    1. (a) \(-12 + 16i\)
    2. (b) \(20\)
    3. (c) \(6.32\)
    1. (a) \(-z = 4 - 3i\): reflection in the origin
    2. (b) \(z^* = -4 - 3i\): reflection in the real axis
    3. (c) \(|z| = |z^*| = |-z| = 5\)
    1. (a) \(25\)
    2. (b) \(5.83\)
    3. (c) \(12\)

In context

    1. (a) 15 m
    2. (b) 24 m

Stretch

    1. (a) \(z = -3 + 4i\) or \(z = -3 - 4i\)
    2. (b) They are conjugates: reflections of each other in the real axis.
    1. (a) Width 10, height 6
    2. (b) Perimeter 32, area 60

jmaths.xyz · AI HL · AHL 6.3 The complex plane and the modulus