IB Mathematics Applications & Interpretation Topic AHL 1.12—complex Numbers Introduction Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 1.12—complex Numbers Introduction Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 1.12—complex Numbers Introduction with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 1.12—complex Numbers Introduction and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

Let $z = x + y i$ be a complex number.

Given that $w = z + 16$ , write down the conjugate of $w$ .

[1]

Use $w \overline{w}$ to express $∣ w ∣^{2}$ in the form $x^{2} + y^{2} + a x + b$ .

[2]

Express $∣ z + 1 ∣^{2}$ in terms of $x$ and $y$ .

[2]

Given that $∣ z + 16∣ = 4∣ z + 1∣$ , find the value of $∣ z ∣$ .

[5]

Question 2

HLPaper 1

Let $z = x + y i$ be a complex number.

Given that $w = z + 16$ , write down the conjugate of $w$ .

[2]

Express $∣ w ∣^{2}$ in the form $x^{2} + y^{2} + a x + b$ .

[2]

Express $∣ z + 1 ∣^{2}$ in terms of $x$ and $y$ .

[2]

Given that $∣ z + 16∣ = 4∣ z + 1∣$ , find the value of $∣ z ∣$ .

[4]

Question 3

HLPaper 1

Consider the quadratic function $f (x) = x^{2} - 8 x + 20$ .

Calculate the discriminant, $Δ$ , of the quadratic function $f (x) = x^{2} - 8 x + 20$ .

[2]

Find the complex roots of the equation $f (x) = 0$ in the form $x = a \pm bi$ using the quadratic formula.

[3]

Rewrite $f (x) = x^{2} - 8 x + 20$ by completing the square, expressing it in the form $f (x) = (x - h)^{2} + k$ .

[2]

Question 4

HLPaper 1

Determine the set of values of the real parameter $m$ for which the equation $(2 m + 1) x^{2} + (m - 4) x + (m + 3) = 0$ has two distinct real roots.

[9]

Question 5

HLPaper 1

Find the complex number $z$ in each of the following equations. Give your answer in the form $a + bi$ , where $a$ and $b$ are real numbers.

Find $z$ such that $(2 + 5 i) z + 9 = 3 + 14 i$ .

[3]

Find $z$ such that $(2 + 5 i) z + 9 = 3 z + 19 i$ .

[3]

Find $z$ such that $(2 + 5 i) z + 8 = 3 \overset{z}{ˉ} + 20 i$ .

[4]

IB Mathematics Applications & Interpretation AHL 1.12—complex Numbers Introduction Questionbank

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IB Mathematics Applications & Interpretation AHL 1.12—complex Numbers Introduction Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 1.12—complex Numbers Introduction Questionbank

Unlock all 22 questions with a free account