JEE Main 2012 Mathematics question

Mathematics Complex Numbers JEE Main 2012

Let Z and W be complex numbers such that |Z| = |W|, and arg Z denotes the principal argument of Z. Statement 1: If arg Z + arg W = π, then . Statement 2: |Z| = |W|, implies .

(1)Statement 1 is true, Statement 2 is false.Correct
(2)Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(3)Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(4)Statement 1 is false, Statement 2 is true.

Answer: (1)

Solution

With and — Statement 1 true. Equal moduli

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Question ID VK-103597