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Question

If z=cosπ4+i sinπ6, then
(a)  z =1,arg(z)=π4
(b)  z =1,arg(z)=π6
(c)  z =32,arg(z)=5π24
(d)  z =32,arg(z)=tan-112


Solution

(d)  z =32, arg (z)=tan-112
z=cosπ4+isinπ6z=12+12iz=122+14z=12+14z=34z=32tan α=Im(z)Re(z)        =12α=tan-112Since, the point z lies in the first quadrant .Therefore, arg(z) =α=tan-112

Mathematics
RD Sharma XI (2015)
Standard XI

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