Practise

Question bank

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

13 questions

SA-9709-P3-CX-0142 marksL1 FoundationCalculatorPolar form

Express

z=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)

in the form

x+iy

, giving exact values.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0022 marksL1 FoundationCalculatorPolar form

Express

z=4\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)

in the form

x+iy

, giving exact values.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0081 markL1 FoundationCalculatorPolar form

e^{i\pi}

equals

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-Q031 markL1 FoundationCalculatorProducts and quotients

For complex numbers

z

and

w

\arg(zw)

equals

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0072 marksL2 StandardCalculatorProducts and quotients

Given

z=2e^{i\pi/3}

and

w=3e^{i\pi/6}

, find

zw

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0082 marksL2 StandardCalculatorProducts and quotients

With

z=2e^{i\pi/3}

and

w=3e^{i\pi/6}

, find the modulus and argument of

\dfrac zw

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0013 marksL2 StandardCalculatorPolar form

Express

-2+2\sqrt3\,i

in the form

re^{i\theta}

, where

r>0

and

-\pi<\theta\le\pi

. State

r

and

\theta

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0032 marksL2 StandardCalculatorProducts and quotients

z=3e^{i\pi/4}

and

w=2e^{-i\pi/12}

. Find the modulus and the argument of

zw

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0042 marksL2 StandardCalculatorProducts and quotients

z=3e^{i\pi/4}

and

w=2e^{-i\pi/12}

. Find the modulus and the argument of

\dfrac zw

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0052 marksL2 StandardCalculatorProducts and quotients

z=2e^{i\pi/3}

. Find

z^3

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0061 markL2 StandardCalculatorProducts and quotients

\arg z=\dfrac{2\pi}3

. The principal argument of

z^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX3-0072 marksL2 StandardCalculatorProducts and quotients

z=2e^{i\pi/5}

. Find the modulus and the argument of

\dfrac1z

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0133 marksL3 ExamCalculatorProducts and quotients

Use the modulus–argument form of

1+i

to find

(1+i)^8

Salam Academy Original Practice · Proposed mark scheme