Mon September 28, 2009 By:

complex numbers

Expert Reply
Wed January 13, 2010

Dear Student

Let A = x+iy  and n is a +ve integer (given)

An=(A+1)n=1+0i  (given)

Taking Modulus

|An|= |(A+1)n|= |1+0i| 

| A|n= |(A+1)|n= 1n    (Since Izn|=|z|n  and 1n =1 for all n)

Taking nth root we get

|A|=|A+1| =1

so x2+y2 =1  and (x+1)2+y2=1

solving we get x=-1/2 and y = 3/2 

Result is independent of n It is true for all n


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