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Question

Find the principal argument of (1+i3).

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Solution

Given that, (1+i3)

z=13+2i3 z=2+2i3 tan α=232=|3|=3 [ tan α=Im(z)Re(z)] tan α=tan π3 α=π3 Re (z)<0 and Im (z)>0 arg(z)=ππ3 =2π3


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