Question:
R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.
R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.
Updated On: Jan 3, 2025
- 20
- 12
- 8
- 13
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The Correct answer is option is (A) : 20
Was this answer helpful?
0
1
Top Questions on Algebra of Complex Numbers
- Find the maximum distance between the two curves: \[ |z-2| = 4 \quad \text{and} \quad |z-2| + |z+2| = 5 \]
- JEE Main - 2026
- Mathematics
- Algebra of Complex Numbers
- If \( 3 \leq |2z + 3(1 + i)| \leq 7 \) and if the maximum and minimum values of \( \left| z + \frac{1}{2}(5 + 3i) \right| \) are \( \alpha \) and \( \beta \) respectively, then \( (\alpha + 2\beta) \) is:
- JEE Main - 2026
- Mathematics
- Algebra of Complex Numbers
- Let \( z \) be the complex number satisfying \( |z - 5| \leq 3 \) and having maximum possible positive argument. Then the value of \[ \left| \frac{5z - 12}{5iz + 16} \right|^2 \] is equal to:
- JEE Main - 2026
- Mathematics
- Algebra of Complex Numbers
- If \( x^2 + x + 1 = 0 \), then \[ \left( x + \frac{1}{x} \right)^4 + \left( x^2 + \frac{1}{x^2} \right)^4 + \left( x^3 + \frac{1}{x^3} \right)^4 + \dots + \left( x^{25} + \frac{1}{x^{25}} \right)^4 \] is
- JEE Main - 2026
- Mathematics
- Algebra of Complex Numbers
Let \( K \) be an algebraically closed field containing a finite field \( F \). Let \( L \) be the subfield of \( K \) consisting of elements of \( K \) that are algebraic over \( F \).
Consider the following statements:
S1: \( L \) is algebraically closed.
S2: \( L \) is infinite.
Then, which one of the following is correct?- GATE MA - 2025
- Mathematics
- Algebra of Complex Numbers
View More Questions
Questions Asked in JEE Main exam
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.- JEE Main - 2026
- Complex Numbers and Quadratic Equations
- The work functions of two metals ($M_A$ and $M_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $M_A$ : $M_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of $M_A$ and $M_B$ are respectively.
- JEE Main - 2026
- Dual nature of matter
- 10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \( P_1 \) to \( P_2 \) is \( \alpha \) Joule \((P_1 = 21.7 \text{ Pa}, P_2 = 30 \text{ Pa}, C_v = 21 \text{ J/K mol}, R = 8.3 \text{ J/mol K})\). The value of \( \alpha \) is ________.
- JEE Main - 2026
- Thermodynamics
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
- The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
- JEE Main - 2026
- Waves and Oscillations
View More Questions