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Further complex numbers — Question 262

Original QCE Vault practice · 5 marks

Q262 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 262 (5 marks)

For this question, the principal argument is Arg⁡z∈(−π,π]\operatorname{Arg}z\in(-\pi,\pi]. Let z,w≠0z,w\ne0.
a)
Use polar form to prove that Arg⁡(zw)=Arg⁡z+Arg⁡w\operatorname{Arg}(zw)=\operatorname{Arg}z+\operatorname{Arg}w modulo 2π2\pi.
[3 marks]
b)
Give a counterexample to the same equation interpreted as literal equality of principal arguments.
[2 marks]
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