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Further complex numbers — Question 261

Original QCE Vault practice · 5 marks

Q261 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 261 (5 marks)

A graphics tool maps a complex number zz to w=(z+2)/(2z+1)w=(z+2)/(2z+1). Assume ∣z∣=1|z|=1.
a)
Show that the mapping is defined for every permitted z.
[2 marks]
b)
Prove that ∣w∣=1|w|=1 for every permitted z.
[3 marks]
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