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Number of solution(s) of the equation |z...

Number of solution(s) of the equation `|z|^2 + 7z = 0` is/are

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I : The number of solutions of the equation z^(2) + |z|^(2) = 0 is 2 II : The number of solutions of z^(2) + |z| = 0 is 3 Which of the statements are true