New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2022 · Shift 1 · Q22

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2022 · Shift 1 · Q22

Complex Numbers question

2022 · Shift 1 · Q22

JEE AdvancedMathematicsComplex NumbersNumerical+3 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

More from Complex Numbers

Let $\overset{z}{ˉ}$ 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 $\overset{z}{ˉ} - z^{2} = i (\overset{z}{ˉ} + z^{2})$ is …2022 · Numerical
Let $\overset{z}{ˉ}$ 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 $(\overset{z}{ˉ})^{2} + \frac{1}{z ^{2}}$ are integers, then which of the following is/are possible…2022 · Multiple correct
Let $θ_{1}, θ_{2}, \dots, θ_{10}$ be positive valued angles (in radian) such that $θ_{1} + θ_{2} + \dots + θ_{10} = 2 π$ . Define the complex numbers $z_{1} = e^{i θ_{1}}, z_{k} = z_{k - 1} e^{i θ_{k}}$ for $k=2,3, \ldots,…2021 · MCQ
For any complex number w = c + id, let $ar g (w) \in (- π, π]$ , where $i = - 1$ . Let $α$ and $β$ be real numbers such that for all complex numbers z = x + iy satisfying $ar g (\frac{z + α}{z + β}) = \frac{π}{4}$ …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 $z^{4} - ∣ z ∣^{4} = 4 i z^{2}$ , where i = $- 1$ . Then the minimum possible value of |z1 $-$ z2|2, where z1, z2 $\in$ S…2020 · Numerical
Let S be the set of all complex numbers z satisfying $∣ z - 2 + i ∣ \geq 5$ . If the complex number z0 is such that $\frac{1}{∣ z _{0} - 1 ∣}$ is the maximum of the set ${\frac{1}{∣ z _{0} - 1 ∣} : z \in S}$ …2019 · MCQ
Let $ω e 1$ be a cube root of unity. Then the minimum of the set ${a + bω + c ω^{2}^{2} : a, b, c$ distinct non-zero integers} equals ..................2019 · Numerical