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 ?

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