Let i=−1, define a sequence of a complex number by z1=0,zn+1=zn2+i for n≥1.In the complex plane, how far from the origin z111 ?

see full answer

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

110

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

z1=0,zn+1=zn2+i,n≥1z2=z12+i at n=1z2=0+i⇒z2=iz3=z22+i⇒z3=i2+i=−1+iz4=z32+i⇒z4=(−1+i)2+i=1+i2−2i+i=−i z5=z42+i⇒ z5=(−i)2+i=−1+iHence,z111=−1+i

Watch 3-min video & get full concept clarity