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 ?

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110

answer is B.

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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

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