wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

Prove that the roots of (z1)n=i(z+1)n when plotted in the Argand plane are collinear.

Open in App
Solution

we have (z1)n=i(z+1)n
|z1|n=|i||z+1|n
or |z1|n=|z+1|n
or |z1|=|z+1|
or |z1|2=|z+1|2
(x1)2+y2=(x+1)2+y2
or 4x=0 or x=0
Therefore, the roots lie on the y-axis.

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