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Question

If θ is the amplitude of a+iba-ib, than tan θ =
(a) 2aa2+b2
(b) 2aba2-b2
(c) a2-b2a2+b2
(d) none of these

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Solution

(b) 2aba2-b2

z=a+iba-ib×a+iba+ibz=a2+i2b2+2abia2-i2b2z=a2-b2+2abia2+b2z=a2-b2a2+b2+i2aba2+b2Rez=a2-b2a2+b2, Imz=2aba2+b2tan α=ImzRez =2aba2-b2α= tan-12aba2-b2Since, z lies in the first quadrant . Therefore, arg (z) =α= tan-12aba2-b2tan θ=2aba2-b2

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