Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Complex Numbers question

2023 · Shift 1 · Q28
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Complex Numbers
  5. /2023 · Shift 1 · Q28

Complex Numbers question

2023 · Shift 1 · Q28

JEE AdvancedMathematicsComplex NumbersNumerical+4 / −1
Let A={1967+1686isin⁡θ7−3icos⁡θ:θ∈R}A=\left\{\frac{1967+1686 i \sin \theta}{7-3 i \cos \theta}: \theta \in \mathbb{R}\right\}A={7−3icosθ1967+1686isinθ​:θ∈R}. If AAA contains exactly one positive integer nnn, then the value of nnn is
Numerical answer
PreviousNext

More from Complex Numbers

  • Let z be a complex number satisfying ∣z∣3+2z2+4zˉ−8=0, where zˉ denotes the complex conjugate of z. Let the imaginary part of z be nonzero. Match each entry in List-I to the correct entries in List-II. The correct… Includes table2023 · MCQ
  • Let z be a complex number with a non-zero imaginary part. If 2−3z+4z22+3z+4z2​ is a real number, then the value of ∣z∣2 is ​.2022 · Numerical
  • Let zˉ denote the complex conjugate of a complex number z and let i=−1​. In the set of complex numbers, the number of distinct roots of the equation zˉ−z2=i(zˉ+z2) is ​…2022 · Numerical
  • Let zˉ 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 (zˉ)2+z21​ are integers, then which of the following is/are possible…2022 · Multiple correct
  • Let θ1​,θ2​,…,θ10​ be positive valued angles (in radian) such that θ1​+θ2​+⋯+θ10​=2π. Define the complex numbers z1​=eiθ1​,zk​=zk−1​eiθk​ for $k=2,3, \ldots,…2021 · MCQ
  • For any complex number w = c + id, let arg(w)∈(−π,π], where i=−1​. Let α and β be real numbers such that for all complex numbers z = x + iy satisfying arg(z+βz+α​)=4π​…2021 · Multiple correct
  • Let S be the set of all complex numbers z satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?2020 · Multiple correct
  • 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 z4−∣z∣4=4iz2, where i = −1​. Then the minimum possible value of |z1 − z2|2, where z1, z2 ∈ S…2020 · Numerical