If c+ic−i = a+ib, where a,b,c are real, then a2+b2 =
c+ic−i = a+ib .........(i)
∴ c−ic+i = a-ib .........(ii)
Multiplying (i) and (ii), we get
c2+1c2+1=a2+b2⇒a2+b2=1.
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