JEE Main Mathematics question
Which of the following statement is true? (i) The amplitude of the product of the two complex numbers is equal to product of their amplitudes. (ii) For any polynomial with real coefficients imaginary roots always occur in conjugate pairs. (iii) Order relation exists in complex numbers whereas it does not exist in real numbers. (iv) The values of used as a cube root of unity and as a fourth root of unity are different.
Solution
(ii) is true (non-real roots of a real polynomial occur in conjugate pairs) and (iv) is true (the non-real cube roots of unity are not among ); (iii) is false, since order exists in the reals and not in the complex numbers. For (i), the amplitude of a product is the sum of the amplitudes,
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