Question:
If (z)2+|z|=0 and if α is sum of roots and β is product of non-zero roots, then find 4(α2+β2)
If (z)2+|z|=0 and if α is sum of roots and β is product of non-zero roots, then find 4(α2+β2)
Updated On: Apr 5, 2024
- \(\frac{1}{4}\)
- 1
- 4
- 2
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct answer is option (C) : 4
Was this answer helpful?
0
0
Top Questions on complex numbers
- Let \( z_1, z_2, z_3 \) be three complex numbers on the circle \( |z| = 1 \) with \( \arg(z_1) = -\frac{\pi}{4}, \arg(z_2) = 0 \) and \( \arg(z_3) = \frac{\pi}{4} \). If \( |z_1 \overline{z_2} + z_2 \overline{z_3} + z_3 \overline{z_1}|^2 = \alpha + \beta \sqrt{2} \), where \( \alpha, \beta \in \mathbb{Z} \), then the value of \( \alpha^2 + \beta^2 \) is :
- JEE Main - 2025
- Mathematics
- complex numbers
- Let integers \( a, b \in [-3, 3] \) be such that \( a + b \neq 0 \). \(\text{Then the number of all possible ordered pairs}\) \( (a, b) \), \(\text{for which}\) \[ \left| \frac{z - a}{z + b} \right| = 1 \quad \text{and} \quad \left| \begin{matrix} z + 1 & \omega & \omega^2 \\ \omega^2 & 1 & z + \omega \\ \omega^2 & 1 & z + \omega \end{matrix} \right| = 1, \] \(\text{is equal to:}\)
- JEE Main - 2025
- Mathematics
- complex numbers
- Let the curve \(z(1 + i) +\) \(\overline{z(1 - i) = 4}\), z \(\in\)\( \mathbb{C}\), divide the region \(|z - 3| \leq 1\) into two parts of areas \( \alpha \) and \( \beta \). Then \( |\alpha - \beta| \) equals:}
- JEE Main - 2025
- Mathematics
- complex numbers
- Let O be the origin, the point A be \( z_1 = \sqrt{3} + 2\sqrt{2}i \), the point B \( z_2 \) be such that \( \sqrt{3}|z_2| = |z_1| \) and \( \arg(z_2) = \arg(z_1) + \frac{\pi}{6} \). Then:
- JEE Main - 2025
- Mathematics
- complex numbers
- Let the curve \((\)\( z(1 + i) + \overline{z(1 - i)} = 4\), \(\, z \in \mathbb{C}\) \()\), divide the region \(|z - 3| \leq 1\) into two parts of areas \( \alpha \) and \( \beta \). Then \( |\alpha - \beta| \) equals:
- JEE Main - 2025
- Mathematics
- complex numbers
View More Questions
Questions Asked in JEE Main exam
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- The distance of the point \( P(1, 2, 3) \) from the plane \( 3x - 4y + 12z - 7 = 0 \) is:
- JEE Main - 2025
- Geometry and Vectors
- A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is \( -3 \), then the magnitude of the radius of curvature of the mirror is:
- JEE Main - 2025
- Spherical Mirrors
- Let the parabola \(y = x^2 + px - 3\) meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1, -1) passes through the points P, Q and R, then the area of \(\triangle PQR\) is:
- JEE Main - 2025
- Coordinate Geometry
- In the circuit shown, assuming the threshold voltage of the diode is negligibly small, then the voltage \( V_{AB} \) is correctly represented by:
- JEE Main - 2025
- Simple diode circuits
View More Questions