1
JEE Advanced 2023 Paper 1 Online
Numerical
+4
-0
Let $A=\left\{\frac{1967+1686 i \sin \theta}{7-3 i \cos \theta}: \theta \in \mathbb{R}\right\}$. If $A$ contains exactly one positive integer $n$, then the value of $n$ is
2
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0
Let $$z$$ be a complex number with a non-zero imaginary part. If

$$\frac{2+3 z+4 z^{2}}{2-3 z+4 z^{2}}$$

is a real number, then the value of $$|z|^{2}$$ is _________.
3
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0
Let $$\bar{z}$$ denote the complex conjugate of a complex number $$z$$ and let $$i=\sqrt{-1}$$. In the set of complex numbers, the number of distinct roots of the equation

$$\bar{z}-z^{2}=i\left(\bar{z}+z^{2}\right)$$

is _________.
4
JEE Advanced 2020 Paper 2 Offline
Numerical
+3
-1
For a complex number z, let Re(z) denote that real part of z. Let S be the set of all complex numbers z satisfying $${z^4} - |z{|^4} = 4i{z^2}$$, where i = $$\sqrt { - 1}$$. Then the minimum possible value of |z1 $$-$$ z2|2, where z1, z2$$\in$$S with Re(z1) > 0 and Re(z2) < 0 is .........