What is the number of distinct solutions of the equation z^2+|z|=0 (where z is a complex number)?

NDA 2016 Mathematics question

What is the number of distinct solutions of the equation (where z is a complex number)?

Answer: (C)

is real and non-positive, so is either 0 or purely imaginary. Put : y^2$+|y| = 0

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Question ID VK-028462