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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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13 questions

SA-9709-P3-CX2-0011 markL1 FoundationCalculatorModulus–argument
Find ∣5−12i∣|5-12i|.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0022 marksL1 FoundationCalculatorModulus–argument
Find the exact argument of −2+2i-2+2i.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0061 markL1 FoundationCalculatorArgand diagram
z=2+iz=2+i. In which quadrant of the Argand diagram is −z∗-z^*?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0071 markL1 FoundationCalculatorArgand diagram
The principal argument of the real number −4-4 is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0091 markL1 FoundationCalculatorModulus–argument
For z=3−5iz=3-5i, find zz∗zz^*.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0111 markL1 FoundationCalculatorArgand diagram
On an Argand diagram, the conjugate z∗z^* is the reflection of zz in
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0023 marksL2 StandardCalculatorModulus–argument
Find the modulus and the exact argument of z=−1+3 iz=-1+\sqrt3\,i.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX-0033 marksL2 StandardCalculatorModulus–argument
Find the modulus of z=−3−4iz=-3-4i, and its argument in radians correct to 3 significant figures, with −π<arg⁡z≤π-\pi<\arg z\le\pi.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0032 marksL2 StandardCalculatorModulus–argument
Find the exact argument of −3−3i-3-3i.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0043 marksL2 StandardCalculatorModulus–argument
Find the modulus and the exact argument of 1−3 i1-\sqrt3\,i.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0052 marksL2 StandardCalculatorModulus–argument
Find the exact value of ∣(3+4i)(1−i)∣|(3+4i)(1-i)|.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0082 marksL2 StandardCalculatorModulus–argument
Find arg⁡(−1−2i)\arg(-1-2i), in radians correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-CX2-0104 marksL4 ChallengingCalculatorModulus–argument
The complex number zz has ∣z∣=5|z|=5 and Re⁡z=−3\operatorname{Re}z=-3, and zz lies above the real axis. Find arg⁡z\arg z, in radians correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme