Request a call back

complex numbers
Asked by | 28 Sep, 2009, 10:08: AM 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 | 13 Jan, 2010, 04:50: PM
CBSE 11-science - Maths
Asked by benganigaurav24 | 10 Jul, 2021, 10:05: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by sahabya | 29 May, 2010, 02:55: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by abhishek11 | 25 May, 2010, 07:11: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by prashant.jain | 24 May, 2010, 12:43: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by sidhusid | 18 May, 2010, 07:14: AM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by MANOJKUMAR | 16 May, 2010, 08:57: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by MANOJKUMAR | 15 May, 2010, 01:33: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by dandirao | 15 May, 2010, 12:19: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by prerana1994 | 11 May, 2010, 08:55: AM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by varunsinghal2011 | 09 May, 2010, 03:45: PM ANSWERED BY EXPERT