Question

anyone plsz answer this, it would be a great help.​

Answer 1

Answer:

Option(a)

Step-by-step explanation:

Given: (1 + i)²ⁿ = (1 - i)²ⁿ

$\Longrightarrow \frac{(1+i)^{2n}}{(1-i)^{2n} } = 1$

$\Longrightarrow (\frac{1+i}{1-i})^{2n} = 1$

$\Longrightarrow (\frac{1+i}{1-i} * \frac{1+i}{1-i})^{2n} = 1$

$\Longrightarrow ({\frac{1-1+2i}{1+1}) ^{2n} = 1$

$\Longrightarrow(\frac{2i}{2})^{2n} = 1$

$\Longrightarrow i^{2n} = 1$

$\Longrightarrow i^{2n} =i^4$

$\Longrightarrow 2n = 4$

$\Longrightarrow n = 2$

Thus, smallest positive integer is 2

Hope it helps!