New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2024 · 8 Apr · Shift 1 · Q48

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

PYQ Library
JEE Main
Mathematics
Complex Numbers
2024 · 8 Apr · Shift 1 · Q48

Complex Numbers question

2024 · 8 Apr · Shift 1 · Q48

JEE MainMathematicsComplex NumbersMCQ+4 / −1

If the set

R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}

has

m

elements and

\sum_{n=1}^m\left(1-i^{n !}\right)=x+i y

, where

i=\sqrt{-1}

, then the value of

m+x+y

is

A
12
B
4
C
8
D
5

More from Complex Numbers

The sum of all possible values of $θ \in [- π, 2 π]$ , for which $\frac{1 + i c o s θ}{1 - 2 i c o s θ}$ is purely imaginary, is equal to :2024 · MCQ
The sum of the square of the modulus of the elements in the set ${z = a + ib : a, b \in Z, z \in C, ∣ z - 1∣ \leq 1, ∣ z - 5∣ \leq ∣ z - 5 i ∣}$ is .2024 · Numerical
Let $z$ be a complex number such that the real part of $\frac{z - 2 i}{z + 2 i}$ is zero. Then, the maximum value of $∣ z - (6 + 8 i) ∣$ is equal to2024 · MCQ
If $S = {z \in C : ∣ z - i ∣ = ∣ z + i ∣ = ∣ z - 1∣}$ , then, $n (S)$ is :2024 · MCQ
If $α$ satisfies the equation $x^{2} + x + 1 = 0$ and $(1 + α)^{7} = A + B α + C α^{2}, A, B, C ⩾ 0$ , then $5 (3 A - 2 B - C)$ is equal to .2024 · Numerical
Let the complex numbers $α$ and $\frac{1}{α ˉ}$ lie on the circles $∣ z - z_{0} ∣^{2} = 4$ and $∣ z - z_{0} ∣^{2} = 16$ respectively, where $z_{0} = 1 + i$ . Then, the value of $100∣ α ∣^{2}$ is .2024 · Numerical
If $z = \frac{1}{2} - 2 i$ is such that $∣ z + 1∣ = α z + β (1 + i), i = - 1$ and $α, β \in R$ , then $α + β$ is equal to2024 · MCQ
Let $α, β$ be the roots of the equation $x^{2} - x + 2 = 0$ with $Im (α) > Im (β)$ . Then $α^{6} + α^{4} + β^{4} - 5 α^{2}$ is equal to .2024 · Numerical