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Question

The principal argument of the complex number z=1+sinπ3+icosπ31+sinπ3icosπ3 is?

A
π3
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B
π6
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C
2π3
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D
π2
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E
π4
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Solution

The correct option is B π6
arg(z)=arg(Numerator)arg(Denominator)
=tan1∣ ∣ ∣cosπ31+sinπ3∣ ∣ ∣+tan1∣ ∣ ∣cosπ31+sinπ3∣ ∣ ∣
=2tan1∣ ∣ ∣cosπ31+sinπ3∣ ∣ ∣
=2tan1(23)=2×15o=π6

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