For n N, let S n = C:|z-3+2 i|=n/4 and T n = C:|z-2+3 i|=1/n. Then the number of elements in the set N: S n T n =φ is:

Complex Numbers and Quadratic Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Morning shift · Q3262

JEE Main 202225 Jul, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

For

\mathrm{n} \in \mathbf{N}

, let

\mathrm{S}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-3+2 i|=\frac{\mathrm{n}}{4}\right\}

and

\mathrm{T}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-2+3 i|=\frac{1}{\mathrm{n}}\right\}

. Then the number of elements in the set

\left\{n \in \mathbf{N}: S_{n} \cap T_{n}=\phi\right\}

is :

JEE Main 2022 · 25 Jul, Morning shift · Q3262

JEE Main 202225 Jul, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

For

\mathrm{n} \in \mathbf{N}

, let

\mathrm{S}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-3+2 i|=\frac{\mathrm{n}}{4}\right\}

and

\mathrm{T}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-2+3 i|=\frac{1}{\mathrm{n}}\right\}

. Then the number of elements in the set

\left\{n \in \mathbf{N}: S_{n} \cap T_{n}=\phi\right\}

is :