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.

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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
Given $z_1 = 2 + 3i$ and $z_2 = 4 - i$ , find
(a) $z_1 + z_2$ , (1 mark)
(b) $z_1 - z_2$ . (1 mark)
Level 1 · 2 marksTry it
2
Expand and simplify $(3 + 2i)(4 - 5i)$ , giving your answer in the form $a + bi$ . (2 marks)
Level 2 · 2 marksTry it
3
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
4
Express $\dfrac{5 + i}{2 - 3i}$ in the form $a + bi$ , where $a$ and $b$ are real. (3 marks)
Level 3 · 3 marksTry it
5
Find the real numbers $x$ and $y$ such that

$(x + yi)(2 - i) = 5 + 5i$ . (4 marks)
Level 3 · 4 marksTry it

12 more questions on complex numbers in cartesian form

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