Let the set of all values of k such that the equation z(z+2+i)+k(2+3i)=0, z, has at least one solution, be the interval [α,β]. Then 9(α+β) is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2026 Mathematics question

JEE Main 2026 · 6 Apr, Morning shift · Q4

JEE Main 20266 Apr, Morning shiftMathematicsEasyComplex Numbers and Quadratic Equations264× since 2002

Let the set of all values of

k\in\mathbb{R}

such that the equation

z(\bar z+2+i)+k(2+3i)=0

z\in\mathbb{C}

, has at least one solution, be the interval

[\alpha,\beta]

. Then

9(\alpha+\beta)

is equal to: