Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
z^n = K (K is real).The sum of the arguments of all the roots of this equation is an odd multiple of pi..When is this possible? That is the relation between n and k.
Dear Aniket,
The sum of all the roots of zn=K is an odd multiple of π when K is negative.
Roots of this equation for K<0 will be z=|K|1/nei(2m+1)π/n where m=0,1,2,...,n-1. Clearly the sum of roots is an odd multiple of π.
e.g. z3=-1
=> z=eiπ/3,eiπ,ei5π/3
Sum of arguments = 3π
Hope this helps.
Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !