if a =cosA+isinA,find the value of (1+a)/(1-a)

Given , a= cosA+isinASo 1+a1-a=1+cosA+isinA1-cosA-isinANow rationalizng the denominator we get, =1+cosA+isinA1-cosA-isinA×1-cosA+isinA1-cosA+isinA=1-cosA+isinA+cosA-cos2A+isinAcosA+isinA-isinAcosA+i2sin2A1-cosA2-i2sin2A=1-cosA+isinA+cosA-cos2A+sin2A+isinA1+cos2A+sin2A-2cosASince i2=-1=1+isinA-1+isinA1+1-2cosASincecos2A+sin2A=1=isinA1-cosA=2isinA2cosA21-1+2sin2A2=icotA2That is purely imaginary.

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