Complex NumbersHard
Question
Let i = √-1 . Define a sequence of complex number by z1 = 0, zn+1 = zn2 + i for n ≥ 1. In the complex plane,
Options
A.1
B.√2
C.√3
D.
Solution
z2 = i
z3 = - 1 + i
z4 = - i
z5 = - 1 + i
z111 = - 1 + i ⇒ |z111| = √ 2
z3 = - 1 + i
z4 = - i
z5 = - 1 + i
z111 = - 1 + i ⇒ |z111| = √ 2
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