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Mathematics · JEE | COMPLEX NUMBERS AND QUADRATIC EQUATIONS
हिन्दीConsider the following properties of modulus and conjugate: (I) \( |z_1 z_2| = |z_1| |z_2| \) (II) \( \overline{z_1 z_2} = \bar{z}_1 \bar{z}_2 \) (III) \( z \bar{z} = |z| \) (IV) \( (\frac{z_1}{z_2}) = \frac{\bar{z}_1}{\bar{z}_2} \) provided \( z_2 \neq 0 \) How many of the above statements are correct?
View Answer & Solution
Correct answer · Option C
Only three
Explanation
Statements (I), (II), and (IV) are correct. Statement (III) is incorrect because \( z \bar{z} = |z|^2 \), not \( |z| \). Thus, exactly three statements are correct.
