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Mathematics · JEE | COMPLEX NUMBERS AND QUADRATIC EQUATIONS
हिन्दीConsider the following statements regarding the history and properties of complex numbers: (I) Mahavira stated in 'Ganitasara Sangraha' that a negative quantity has no square root. (II) Euler introduced the symbol \( i \) for \( \sqrt{-1} \). (III) W.R. Hamilton regarded complex numbers as ordered pairs of real numbers. (IV) The product of a complex number and its conjugate is always negative. How many of the above statements are correct?
View Answer & Solution
Correct answer · Option C
Only three
Explanation
Statements (I), (II), and (III) are historically and mathematically correct. Statement (IV) is incorrect because \( z\bar{z} = |z|^2 \ge 0 \), which is non-negative.
