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Question

For n an integer, the argument of
Z=(3+i)4n+1(1i3)4n is

A
π6
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B
π3
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C
π2
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D
2π3
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Solution

The correct option is B π6

Z=(1+3ii)4n+1(1i3)4n


Z=(2ωi)4n+1(2ω)4n


=2ωi4n+1×(2ω2ω)4n


=2ωi×1


=1+3ii


=3+i
arg|z|=tan1(13)
=π6


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