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Further complex numbers — Question 265

Original QCE Vault practice · 6 marks

Q265 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 265 (6 marks)

For z≠0z\ne0, use Arg⁡z∈(−π,π]\operatorname{Arg}z\in(-\pi,\pi]. Define R={z:1≤∣z∣≤2, 0<Arg⁡z≤π/2}R=\{z:1\le|z|\le2,\ 0<\operatorname{Arg}z\le\pi/2\}.
Question 118 stimulus; see the question for exact data and required construction.
a)
Sketch and shade R. Indicate which boundaries are included or excluded.
[4 marks]
b)
Determine all roots of z4=16z^4=16 that belong to R, explaining each boundary decision.
[2 marks]
Question linkSyllabus coverage

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