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Question

If z(223i)2=i(3+i)4, then arg(z) is

A
5π6
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B
π6
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C
π6
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D
2π3
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Solution

The correct option is C π6
z(223i)2=i(3+i)4
arg(z(223i)2)=arg(i(3+i)4)arg(z)+2arg(223i)=arg(i)+4arg(3+i)+2kπ,kZarg(z)+2(π3)=π2+4(π6)+2kπ,kZarg(z)=11π6+2kπ,kZ
If k=1
arg(z)=π6(π,π]
arg(z)=π6

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