Q56 / 90 · JEE Main 2018 (16 Apr Online) · Mathematics

The least positive integer $n$ for which ${(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1$ is

A
$2$
B
$5$
C
$6$
Correct answer
D
$3$

Solution

Given

{(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1

⇒

{(\frac{- 2 ω^{2}}{- 2 ω})}^{n} = 1

\Rightarrow

ω^{n} = 1

Hence, the least positive integer value of

n

is

3

.

Hence, the correct answer is option: 'D'.

Relevant Questions

Let the set of all values of such that the equation , , has at least one solution, be the interval . Then is equal to:06 Apr, 2026 (M)Algebra of complex numbers
Let and be real numbers such that , . Then the value of is :02 Apr, 2026 (M)Algebra of complex numbers
Let the product of and be , . Let p and q be the maximum and the minimum values of respectively.04 Apr, 2025 (E)Algebra of complex numbers
Let be such that . Then the sum of all possible values of is03 Apr, 2025 (M)Algebra of complex numbers
If and are the roots of , then is equal to :28 Jan, 2025 (E)Algebra of complex numbers
The number of complex numbers , satisfying and , is :23 Jan, 2025 (E)Algebra of complex numbers