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Complex Numbers question

2024 · 31 Jan · Shift 1 · Q51

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JEE Main
Mathematics
Complex Numbers
2024 · 31 Jan · Shift 1 · Q51

Complex Numbers question

2024 · 31 Jan · Shift 1 · Q51

JEE MainMathematicsComplex NumbersNumerical+4 / −1

If

\alpha

denotes the number of solutions of

|1-i|^x=2^x

and

\beta=\left(\frac{|z|}{\arg (z)}\right)

, 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], i=\sqrt{-1}

, then the distance of the point

(\alpha, \beta)

from the line

4 x-3 y=7

is

\underline{\hspace{2cm}}

.

Numerical answer

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