QJEEM20Ma2e76: JEE Main 2020 Mathematics - Class 11 JEEM20Ma2e76 Solution: The region represented by {z = x + iy ∈ C :

Question

Verified Solution • 2025–26 Session moderate

The region represented by
{z = x + iy

\in

C : |z| – Re(z)

\leq

1} is also given by the
inequality : {z = x + iy

\in

C : |z| – Re(z)

\leq

1}

Accepted Answer

Given z = x + iy

|z| – Re(z)

\leq

1

\Rightarrow

\sqrt{x^{2} + y^{2}}

- x

\leq

1

\Rightarrow

\sqrt{x^{2} + y^{2}}

\leq

1 + x

\Rightarrow

x² + y²

\leq

1 + 2x + x²

\Rightarrow

y²

\leq

2x + 1

\Rightarrow

y²

\leq

2

(x + \frac{1}{2})

Step-by-Step Verified Solution