QJEEM24Ma4069: JEE Main 2024 Mathematics - Class 11 JEEM24Ma4069 Solution: If α denotes the number of solutions of

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QJEEM24Ma4069: JEE Main 2024 Mathematics - Class 11 JEEM24Ma4069 Solution: If α denotes the number of solutions of

If $α$ denotes the number of solutions of $| 1 - i |^{x} = 2^{x}$ and $β = (\frac{| z |}{\arg (z)})$ , where $z = \frac{π}{4} (1 + i)^{4} [\frac{1 - \sqrt{π} i}{\sqrt{π} + i} + \frac{\sqrt{π} - i}{1 + \sqrt{π} i}], i = \sqrt{- 1}$ , then the distance of the point $(α, β)$ from the line $4 x - 3 y = 7$ is __________.

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Accepted Answer

$\begin{aligned} (\sqrt{2})^{x} = 2^{x} \Rightarrow x = 0 \Rightarrow α = 1 \\ z = \frac{π}{4} (1 + i)^{4} [\frac{\sqrt{π} - π i - i - \sqrt{π}}{π + 1} + \frac{\sqrt{π} - i - π i - \sqrt{π}}{1 + π}] \\ = - \frac{π i}{2} (1 + 4 i + 6 i^{2} + 4 i^{3} + 1) \\ = 2 π i \\ β = \frac{2 π}{\frac{π}{2}} = 4 \end{aligned}$

Distance from $(1, 4)$ to $4 x - 3 y = 7$

Will be $\frac{15}{5} = 3$

QJEEM24Ma4069: JEE Main 2024 Mathematics - Class 11 JEEM24Ma4069 Solution: If α denotes the number of solutions of

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