The least positive integer n for which $(1 + i)^{n} = (1 - i)^{n}$ holds is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 4
$(i + i)^{n} = (1 - i)^{n}$
$\Rightarrow {(\frac{1 + i}{1 - i})}^{n} = 1$
$\Rightarrow \frac{1 + i}{1 - i} = \frac{1 + i}{1 - i} \frac{1 + i}{1 + i}$
$= \frac{1 - 1 + 2 i}{1 - (- 1)} = \frac{2 i}{2} = i$
$\Rightarrow i^{n} = 1$
since, $i^{4} = 1$
So, $n = 4$

Suggest Corrections

Similar questions

n

n! < {(\frac{n + 1}{2})}^{n}

n

n! < {(\frac{n + 1}{2})}^{n}

3^{n + 1} < 4^{n}

\sqrt{n + 1} - \sqrt{n - 1} < 0.2

n

{(\frac{1 + i}{1 - i})}^{n}

Join BYJU'S Learning Program