Let z satisfy |z| = 1 and z = 1 - z. Statement 1 : z is a real number. Statement 2 : Principal argument of z is 3 .

JEE Main 2013 Mathematics question

Let z satisfy |z| = 1 and . Statement 1 : z is a real number. Statement 2 : Principal argument of z is .

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

Answer: (2)

With z = x + iy, gives . With |z| = 1, , so \frac$12 ±

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Question ID VK-104226