Medium MCQ +4 / -1 PYQ · JEE Mains 2020

The region represented by
{z = x + iy $\in$ C : |z| – Re(z) $\le$ 1} is also given by the
inequality : {z = x + iy $\in$ C : |z| – Re(z) $\le$ 1}

A y2 $\le$ $2\left( {x + {1 \over 2}} \right)$ Correct answer
B y2 $\le$ ${x + {1 \over 2}}$
C y2 $\ge$ 2(x + 1)
D y2 $\ge$ x + 1

Solution

Given z = x + iy |z| – Re(z) $\le$ 1 $\Rightarrow$ $\sqrt {{x^2} + {y^2}}$ - x $\le$ 1 $\Rightarrow$ $\sqrt {{x^2} + {y^2}}$ $\le$ 1 + x $\Rightarrow$ x2 + y2 $\le$ 1 + 2x + x2 $\Rightarrow$ y2 $\le$ 2x + 1 $\Rightarrow$ y2 $\le$ 2$\left( {x + {1 \over 2}} \right)$

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Subject: Mathematics · Chapter: Complex Numbers and Quadratic Equations · Topic: Complex Numbers and Argand Plane

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The region represented by {z = x + iy $\in$ C : |z| – Re(z) $\le$ 1} is also given by the inequality : {z = x + iy $\in$ C : |z| – Re(z) $\le$ 1}

Solution

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The region represented by
{z = x + iy $\in$ C : |z| – Re(z) $\le$ 1} is also given by the
inequality : {z = x + iy $\in$ C : |z| – Re(z) $\le$ 1}