IB Maths AI HL AI 1.4 Complex numbers questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1 Paper 2

Difficulty

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Question 1

Paper 1Easy6 marks

A point $P$ on an Argand diagram is represented by $z=1+2i$

(a)

Write down the real part and the imaginary part of $z$

[2]

(b)

Write down the complex conjugate of $z$

[1]

(c)

Determine the distance of $P$ from the origin, in units.

[1]

(d)

Use your GDC to calculate $z^3$ giving your answer in Cartesian form.

[2]

Question 2

Paper 1Medium6 marks

The equation $x^2-8x+25=0$ has roots $z$ and $\bar z$ where $\operatorname{Im}(z)>0$

(a)

Find $z$ in Cartesian form.

[2]

(b)

Let

q=\frac{z-2}{\bar z-2}.

Find $q$ in Cartesian form.

[2]

(c)

Find the modulus and principal argument of $q$ Give the argument in radians, correct to three significant figures, in the range $-\pi<\arg(q)\leq\pi$

[2]

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