Leaving Cert Maths: Complex numbers
How often Complex numbers comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Quick ones on Complex numbers.
- 1
- −1
- i
- −3 − 2i
- −3 + 2i
- 3 + 2i
- 10
- 100
- 14
Show the answers
(a) −1
(b) 3 + 2i
(c) 10
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q4 |
| 2025 | Q4 |
| 2024 | Q2 |
| 2023 | Q4 |
| 2022 | Q3 |
| 2021 | Q1 |
| 2019 | Q5 |
| 2018 | Q4 |
| 2017 | Q2 |
| 2016 | Q1 |
Links open the State Examinations Commission’s paper for that year.
More Complex numbers questions
Complex numbers, 2 marks
Argument of i?
- 0
- π
- π/2
Show the answer
π/2
i = 0 + 1i sits on the positive imaginary axis, which is 90° = π/2 from the positive real axis.
Complex numbers, 2 marks
Multiplying a complex number by i rotates it by …
- 180°
- 90° anticlockwise
- 90° clockwise
Show the answer
90° anticlockwise
i has modulus 1 and argument 90°, so multiplying by i keeps the modulus and adds 90° to the argument. E.g. 1 × i = i.
Complex numbers, 2 marks
Modulus of z = −5?
- 5
- −5
- 25
Show the answer
5
−5 = −5 + 0i, so |z| = √((−5)² + 0²) = 5. Modulus is distance from 0, so it's never negative.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q4 |
| 2025 | Q2 |
| 2024 | Q2 |
| 2023 | Q2 |
| 2022 | Q1 |
| 2021 | Q2 |
| 2019 | Q2 |
| 2018 | Q2 |
| 2017 | Q2 |
| 2016 | Q2 |
Links open the State Examinations Commission’s paper for that year.
More Complex numbers questions
Complex numbers, 2 marks
Which point on an Argand diagram represents 3 − 2i?
- (−2, 3)
- (3, 2)
- (3, −2)
Show the answer
(3, −2)
The real part goes across and the imaginary part goes up. 3 − 2i has real part 3 and imaginary part −2, so it is the point (3, −2).
Complex numbers, 2 marks
The point (−4, 1) is plotted on an Argand diagram. Which complex number is it?
- −4 − i
- −4 + i
- 1 − 4i
Show the answer
−4 + i
Across is the real part, −4, and up is the imaginary part, 1. So the number is −4 + 1i, written −4 + i.
Complex numbers, 2 marks
On an Argand diagram, the number 5i lies on …
- the imaginary axis
- the real axis
- neither axis
Show the answer
the imaginary axis
5i = 0 + 5i. The real part is 0, so the point (0, 5) sits on the vertical axis, which is the imaginary axis.