wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let a sequence x1,x2,x3,... of complex number be defined by x1=0,xn+1=x2ni for n>1 where i2=1. Find the distance of x2000 from x1997 in the complex plane. If the distance is k, then find k2.

Open in App
Solution

x1=0
x2=02i=i
x3=(i)2i=1i=(1+i)
x4=[(1+i)]2i=2ii=i
x5=(i)2i=1i=x3
x6=x4 and hence x7=x5 and so on,
x2n=i, x2n+1=(1+i)
x2000=i=(0,1) and x1997=1i=(1,1) in the complex plane.
So, the distance between x2000 and x1997 is 1+4=5.
k2=5

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon