Practise

Question bank

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

TopicSkillDifficulty

14 questions

SA-9709-P3-CX-0012 marksL1 FoundationCalculatorArithmetic

Express

(2-3i)^2

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0011 markL1 FoundationCalculatorArithmetic

Express

(4+3i)+(2-5i)-(1-i)

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0022 marksL1 FoundationCalculatorArithmetic

Express

(3+2i)(4-i)

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0041 markL1 FoundationCalculatorArithmetic

i^7

equals

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-G014 marksL1 FoundationCalculatorArithmetic

Given

z=3+2i

and

w=1-i

, find

zw

and

\dfrac zw

, each in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-Q011 markL1 FoundationCalculatorArithmetic

i^2

equals

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-Q021 markL1 FoundationCalculatorArithmetic

The conjugate of

3-4i

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX-0123 marksL2 StandardCalculatorEquating parts

Find the complex number

z

such that

z(2-i)=7+i

, giving your answer in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0033 marksL2 StandardCalculatorArithmetic

Express

\dfrac{5+i}{2-3i}

in the form

x+iy

, giving

x

and

y

as fractions.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0053 marksL2 StandardCalculatorEquating parts

The real numbers

x

and

y

satisfy

(x+iy)(1+2i)=7+4i

. Find

x

and

y

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0063 marksL2 StandardCalculatorArithmetic

Given

z=2-i

, express

z^2+z^*

in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0072 marksL2 StandardCalculatorArithmetic

Find the value of

\dfrac{1}{1+i}+\dfrac{1}{1-i}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0093 marksL3 ExamCalculatorEquating parts

Find the real numbers

a

and

b

such that

(a+bi)^2=-5+12i

, given that

a>0

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-CX1-0084 marksL4 ChallengingCalculatorEquating parts

Find the complex number

z

such that

z+2z^*=6-3i

, giving your answer in the form

x+iy

Salam Academy Original Practice · Proposed mark scheme