Browse Complex numbers

79 questions at your level, grouped by concept

DifficultyAllLevel 1Level 2Level 3Level 4Level 5

Complex numbers in Cartesian form

17 questions

LessonNot started
  1. 1
    Given z1=2+3iz_1 = 2 + 3i and z2=4−iz_2 = 4 - i, find
    (a) z1+z2z_1 + z_2, (1 mark)
    (b) z1−z2z_1 - z_2. (1 mark)
    Level 1 · 2 marksTry it

The Argand diagram, modulus and argument

15 questions

LessonNot started
  1. 1
    Find the modulus of the complex number z=8+6iz = 8 + 6i. (2 marks)
    Level 1 · 2 marksTry it

Complex roots of polynomial equations

15 questions

LessonNot started
  1. 1
    Solve the equation z2−4z+13=0z^2 - 4z + 13 = 0, giving your answers in the form a+bia + bi where aa and bb are real. (3 marks)
    Level 1 · 3 marksTry it

Loci in the Argand diagram

16 questions

LessonNot started
  1. 1
    Describe fully the locus of points in the Argand diagram given by ∣z−(2+i)∣=3|z - (2 + i)| = 3. (2 marks)
    Level 1 · 2 marksTry it

Modulus–argument (polar) form

16 questions

LessonNot started
  1. 1
    The complex number z=1+3 iz = 1 + \sqrt{3}\,i.
    (a) Find ∣z∣|z|. (1 mark)
    (b) Find arg⁡z\arg z, and hence express zz in the form r(cos⁡θ+isin⁡θ)r(\cos\theta + i\sin\theta), where −π<θ≤π-\pi < \theta \le \pi. (2 marks)
    Level 1 · 3 marksTry it