JEE PYQ: Complex Numbers Question 22
Question 22 - 2020 (06 Sep Shift 1)
The region represented by ${z = x + iy \in \mathbb{C} : |z| - \text{Re}(z) \le 1}$ is also given by the inequality:
(1) $y^2 \ge 2(x+1)$
(2) $y^2 \le 2\left(x + \frac{1}{2}\right)$
(3) $y^2 \le x + \frac{1}{2}$
(4) $y^2 \ge x + 1$
Show Answer
Answer: (2)
Solution
$\sqrt{x^2+y^2} - x \le 1 \Rightarrow \sqrt{x^2+y^2} \le 1 + x$ (need $x \ge -1$). Squaring: $y^2 \le 2x + 1 = 2(x + \frac{1}{2})$.
BETA
