1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of $$(\bar{z})^{2}+\frac{1}{z^{2}}$$ are integers, then which of the following is/are possible value(s) of $|z|$ ?
A
$\left(\frac{43+3 \sqrt{205}}{2}\right)^{\frac{1}{4}}$
B
$\left(\frac{7+\sqrt{33}}{4}\right)^{\frac{1}{4}}$
C
$\left(\frac{9+\sqrt{65}}{4}\right)^{\frac{1}{4}}$
D
$\left(\frac{7+\sqrt{13}}{6}\right)^{\frac{1}{4}}$
2
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
For any complex number w = c + id, let $$\arg (w) \in ( - \pi ,\pi ]$$, where $$i = \sqrt { - 1}$$. Let $$\alpha$$ and $$\beta$$ be real numbers such that for all complex numbers z = x + iy satisfying $$\arg \left( {{{z + \alpha } \over {z + \beta }}} \right) = {\pi \over 4}$$, the ordered pair (x, y) lies on the circle $${x^2} + {y^2} + 5x - 3y + 4 = 0$$, Then which of the following statements is (are) TRUE?
A
$$\alpha$$ = $$-$$1
B
$$\alpha$$$$\beta$$ = 4
C
$$\alpha$$$$\beta$$ = $$-$$4
D
$$\beta$$ = 4
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let S be the set of all complex numbers z
satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?
A
$$\left| {z + {1 \over 2}} \right|$$ $$\le$$ $${{1 \over 2}}$$ for all z$$\in$$S
B
|z| $$\le$$ 2 for all z$$\in$$S
C
$$\left| {z + {1 \over 2}} \right|\, \ge {1 \over 2}$$ for all z$$\in$$S
D
The set S has exactly four elements
4
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let s, t, r be non-zero complex numbers and L be the set of solutions $$z = x + iy(x,y \in R,\,i = \sqrt { - 1} )$$ of the equation $$sz + t\overline z + r = 0$$ where $$\overline z$$ = x $$-$$ iy. Then, which of the following statement(s) is(are) TRUE?
A
If L has exactly one element, then |s|$$\ne$$|t|
B
If |s| = |t|, then L has infinitely many elements
C
The number of elements in $$L \cap \{ z:|z - 1 + i| = 5\}$$ is at most 2
D
If L has more than one element, then L has infinitely many elements
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