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complex numbers

Asked by 28th September 2009, 10:08 AM
Answered by Expert
Answer:

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

Regards

Team Topperlearning

 

 

 

Answered by Expert 13th January 2010, 4:50 PM
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