A mathematical problem on the complex number! If the complex number Z1 satisfies Z1 = I (2-z1) (I is an imaginary unit), if | Z | = 1, find the maximum value of | z-z1 |

A mathematical problem on the complex number! If the complex number Z1 satisfies Z1 = I (2-z1) (I is an imaginary unit), if | Z | = 1, find the maximum value of | z-z1 |

Let Z1 = a + bi, where a and B are real numbers, then Z1 = I (2-z1) can be written as: a + bi = I (2-a-bi)
If a + bi = B + (2-A) I, the corresponding terms of the left and right expressions are equal
If a = B, B = 2-A, then a = b = 1
That is Z1 = 1 + I
|Z-Z1|

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