1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
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
Change Language
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
Change Language
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
JEE Advanced Subjects
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEEBITSAT
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN