GCE Advanced Level (Sri Lanka) · Combined Mathematics

Pure Maths: Complex Numbers and Trigonometry

41 practice questions, each with the answer and an explanation.

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All 41 questions

Find the maximum value of $32 sin θ + 60 cos θ$ .
How many solutions does $2 sin x = 1$ have for $0 \leq x \leq 2 π$ ?
Find $(1 + i)^{2}$ .
If $sin A = \frac{3}{5}$ and $A$ is acute, find $cos 2 A$ .
Find the sum of the solutions of $tan x = 1$ in the interval $0 \leq x < 2 π$ , in terms of $π$ .
Find the value of $(1 + 5 i) (1 - 5 i)$ .
If $sin A = \frac{5}{13}$ and $A$ is acute, find $cos 2 A$ .
Find $(1 + i)^{8}$ .
Find the maximum value of $10 sin θ + 24 cos θ$ .
Find the value of $(4 + 3 i) (4 - 3 i)$ .
Find the modulus of $z = 7 + 24 i$ .
Find $(1 + i)^{6}$ .
Find the maximum value of $14 sin θ + 48 cos θ$ .
If $z = - 5 - 2 i$ and $w = - 4 - i$ , find the real part of $z w$ .
Find the maximum value of $9 sin θ + 12 cos θ$ .
Find the value of $(3 + i) (3 - i)$ .
Find the value of $(2 + 3 i) (2 - 3 i)$ .
Find the modulus of $z = 7 - 24 i$ .
Find the modulus of $z = 5 - 12 i$ .
Find the maximum value of $24 sin θ + 45 cos θ$ .
Find the value of $(1 + 3 i) (1 - 3 i)$ .
If $z = - 3 - 2 i$ and $w = 4 - i$ , find the real part of $z w$ .
Find the maximum value of $3 sin θ + 4 cos θ$ .
Find the maximum value of $28 sin θ + 96 cos θ$ .
Find the modulus of $z = 8 + 15 i$ .
Find the maximum value of $15 sin θ + 36 cos θ$ .
Find the modulus of $z = 3 - 4 i$ .
If $z = - 5 - 2 i$ and $w = 0 + 3 i$ , find the real part of $z w$ .
Find the value of $(1 + 2 i) (1 - 2 i)$ .
Find $(1 + i)^{4}$ .
If $z = 2 - i$ and $w = 2 - 4 i$ , find the real part of $z w$ .
If $z = - 5 + 5 i$ and $w = - 5 + 3 i$ , find the real part of $z w$ .
Find the maximum value of $16 sin θ + 30 cos θ$ .
If $sin A = \frac{7}{25}$ and $A$ is acute, find $cos 2 A$ .
If $z = 4 + 2 i$ and $w = 4 - 5 i$ , find the real part of $z w$ .
Find the value of $(1 + 4 i) (1 - 4 i)$ .
Find the value of $(4 + i) (4 - i)$ .
Find the maximum value of $7 sin θ + 24 cos θ$ .
If $sin A = \frac{8}{17}$ and $A$ is acute, find $cos 2 A$ .
Find the maximum value of $5 sin θ + 12 cos θ$ .
Find the maximum value of $8 sin θ + 15 cos θ$ .

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