Question

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

• A. $2$
• B. $5$
• C. $6$
• D. $3$

Answer 1

The correct option is D $3$

${\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)}^n=1\Rightarrow {\left(\frac{-2{\omega }^2}{-2\omega }\right)}^n=1\left(\omega \text{is cube root of unity}\right)\Rightarrow {\omega }^n=1$
So, the least positive value of $n=3$