i'll give u the easiest & shortest way.

 

|z^2 -1|=|z|^2 + 1    [given]

or, we can say that, | z^2 +(-1)|  =  |z^2| + |-1|

 

it shows that the origin , -1 & z^2 lies  on a line & z^2 & -1 lies on one side of the origin, therefore z^2 is a negative number. hence z  will be purely imaginary. so we can also say that z lies on y-axis.

 

 

answer: 2)imaginary

 

 

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