1
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 _________.
2
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 _________.
3
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 .........
4
JEE Advanced 2019 Paper 1 Offline
Numerical
+3
-0 Let $$\omega \ne 1$$ be a cube root of unity. Then the maximum of the set $$\{ {\left| {a + b\omega + c{\omega ^2}} \right|^2}:a,b,c$$ distinct non-zero integers} equals ..................
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