Let Z and W be two complex numbers such that \[\left| Z \right|\le 1,\] \[\left| W \right|\le 1\] and \[\left| Z+i\,W \right|=\left| Z-i\overline{W} \right|=2.\] Then Z equals

Let Z and W be two complex numbers such that \[\left| Z \right|\le 1,\

1.	Let Z and W be two complex numbers such that \[\left\| Z \right\|\le 1,\] \[\left\| W \right\|\le 1\] and \[\left\| Z+i\,W \right\|=\left\| Z-i\overline{W} \right\|=2.\] Then Z equals
A.	1 or i
B.	i or \[-i\]
C.	1 or \[-i\]
D.	i or \[-1\]
Answer» D. i or \[-1\]

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Let Z and W be two complex numbers such that \[\left| Z \right|\le 1,\] \[\left| W \right|\le 1\] and \[\left| Z+i\,W \right|=\left| Z-i\overline{W} \right|=2.\] Then Z equals

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