Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/complex-numbers/ahl-6-3/problems/b/

jmaths

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

The complex plane and the modulus Problem set B Answers

Skills

    1. (a) \(-z = 5 - 4i\)
    2. (b) \(z^* = -5 - 4i\)
    3. (c) \(-z^* = 5 + 4i\): reflection in the imaginary axis
    1. (a) \(16 - 12i\)
    2. (b) \(20\)
    3. (c) \(10.8\)
    1. (a) \(-z = -6 + 8i\): reflection in the origin
    2. (b) \(z^* = 6 + 8i\): reflection in the real axis
    3. (c) \(|z| = |z^*| = |-z| = 10\)
    1. (a) \(17\)
    2. (b) \(7.21\)
    3. (c) \(7\)

In context

    1. (a) 17 mm
    2. (b) 34 mm

Stretch

    1. (a) \(z = 5 + 12i\) or \(z = 5 - 12i\)
    2. (b) They are conjugates: reflections of each other in the real axis.
    1. (a) Width 8, height 14
    2. (b) Perimeter 44, area 112

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