New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2024 · 29 Jan · Shift 2 · Q55

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

PYQ Library
JEE Main
Mathematics
Complex Numbers
2024 · 29 Jan · Shift 2 · Q55

Complex Numbers question

2024 · 29 Jan · Shift 2 · Q55

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

\alpha, \beta

be the roots of the equation

x^2-\sqrt{6} x+3=0

such that

\operatorname{Im}(\alpha)\gt \operatorname{Im}(\beta)

. Let

a, b

be integers not divisible by 3 and

n

be a natural number such that

\frac{\alpha^{99}}{\beta}+\alpha^{98}=3^n(a+i b), i=\sqrt{-1}

. Then

n+a+b

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Complex Numbers

If $z = x + i y, x y e q 0$ , satisfies the equation $z^{2} + i \overset{z}{ˉ} = 0$ , then $z^{2}$ is equal to :2024 · MCQ
If $z$ is a complex number, then the number of common roots of the equations $z^{1985} + z^{100} + 1 = 0$ and $z^{3} + 2 z^{2} + 2 z + 1 = 0$ , is equal to2024 · MCQ
If $α$ denotes the number of solutions of $∣1 - i ∣^{x} = 2^{x}$ and $β = (\frac{∣ z ∣}{a r g ( z )})$ , where $$z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi} i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} i}\right],…2024 · Numerical
Let $z_{1}$ and $z_{2}$ be two complex numbers such that $z_{1} + z_{2} = 5$ and $z_{1}^{3} + z_{2}^{3} = 20 + 15 i$ Then, $z_{1}^{4} + z_{2}^{4}$ equals -2024 · MCQ
If the center and radius of the circle $\frac{z - 2}{z - 3} = 2$ are respectively $γ$ and $γ$ , then $3 (α + β + γ)$ is equal to :2023 · MCQ
Let $a, b$ be two real numbers such that $ab < 0$ . IF the complex number $\frac{1 + ai}{b + i}$ is of unit modulus and $a + ib$ lies on the circle $∣ z - 1∣ = ∣2 z ∣$ , then a possible value of $\frac{1 + [ a ]}{4 b}$ , where $[t]$ is greatest integer…2023 · MCQ
Let $a e q b$ be two non-zero real numbers. Then the number of elements in the set $X = {z \in C : Re (a z^{2} + b z) = a$ and $Re (b z^{2} + a z) = b}$ is equal…2023 · MCQ
For $α, β, z \in C$ and $λ > 1$ , if $λ - 1$ is the radius of the circle $∣ z - α ∣^{2} + ∣ z - β ∣^{2} = 2 λ$ , then $∣ α - β ∣$ is equal to .2023 · Numerical