Let \(z_1\) and \(z_2\) be two complex numbers such that \(z_1 + z_2 = 5\) and \(z_1^3+z_2^3 =20 +15i\), then the value of \(| z_1^4+z_2^4 |\) is equal to
\(75\)
\(15\sqrt {15}\)
\(25\sqrt {5}\)
\(30\sqrt 3\)
The Correct Option is A
Solution and Explanation
The correct option is (A): \(75\).
Top Questions on complex numbers
- If \(r = |z|,\ θ = arg(z)\) and \( z = 2 – 2\ tan (\frac {5\pi}{8})\) then find \((r, θ)\).
- JEE Main - 2024
- Mathematics
- complex numbers
- If \(z = x + iy, \quad xy \neq 0\) satisfies the equation \(z^2 + iz = 0\), then \(|z^2|\); equal to
- JEE Main - 2024
- Mathematics
- complex numbers
- Let f(x) = x4 + ax3 + bx2 + c be a polynomial with real coefficients such that f(1) = -9. Suppose that \(i\sqrt3\) is a root of the equation 4x3 + 3ax2 + 2bx = 0, where\(i=\sqrt{-1}\) . If a1, a2, a3 and a4 are all the roots of the equation f(x) = 0, then |a1|2 + |a2|2 + |a3|2 + |a4|2 is equal to ______.
- JEE Advanced - 2024
- Mathematics
- complex numbers
- If : \(|z + 1| = αz + ß(i + 1)\) and \(z = \frac 12 - 2i\), find \(α + ß\).
- JEE Main - 2024
- Mathematics
- complex numbers
Consider the lines $L_1$ and $L_2$ given by
$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $
$ L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$
A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is
- JEE Main - 2023
- Mathematics
- complex numbers
Questions Asked in JEE Main exam
- An electron in the 5th excited state of He+ atom moves to the 1st excited state. Find the number of possible spectral lines formed.
- JEE Main - 2024
- Atomic Spectra
- In given circuit, reading of voltmeter is 1 V, then resistance of
- JEE Main - 2024
- Heat Transfer
- We are given with three NaCl samples and their Van't Hoff factors. Which is correct option ?
Sample Van't Haff Factor Sample - 1 (0.1 M) \(i_1\) Sample - 2 (0.01 M) \(i_2\) Sample - 3 (0.001 M) \(i_2\) - JEE Main - 2024
- Solutions
- Complementary stand of DNA ATGCTTCA is:
- JEE Main - 2024
- Hydrogen Bonding
- Which is following compound is easily attacked by electrophile?
- JEE Main - 2024
- Organic Chemistry- Some Basic Principles and Techniques
JEE Main Notification
JEE Main 2025 Chapter-wise Question Papers Available, Download HereSep 09, 2024Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.
SUBSCRIBE TO OUR NEWS LETTER
