A-level · Complex numbers

Complex numbers in Cartesian formExam-style questions

The imaginary unit i with i² = −1, real and imaginary parts, equality of complex numbers, and the four operations in the form a + bi — addition, subtraction, multiplication, and division by realising the denominator with the conjugate.

Start practising Read the lesson

17 questions · A Level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Expand and simplify $(3 + 2i)(4 - 5i)$ , giving your answer in the form $a + bi$ . (2 marks)
Level 2 · 2 marksTry it
2
The complex number $z = 5 - 2i$ , and $z^{*}$ denotes its conjugate.
(a) Find $zz^{*}$ . (2 marks)
(b) Write down $z + z^{*}$ and $z - z^{*}$ . (2 marks)
Level 2 · 4 marksTry it