Question

I. lf a and $b$ are positive real numbers then $\sqrt{-a}\sqrt{-b}=\sqrt{ab}$
II. The argument of $\frac{1+i\sqrt{3}}{1-i\sqrt{3}}$ is $240$

Which of the above statements is true?

• A. only $I$ is true
• B. Only $II$ is true
• C. both $I$ and $II$ are true
• D. Neither $I$ nor $II$ are true

Answer 1

Answer: (A)

only $I$ is true

Statement-I is correct.

$arg\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)$

Multiplying and dividing by $1+i\sqrt{3}$,

$arg\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)=arg(\frac{-1}{2}$ + $\frac{i\sqrt{3}}{2}$)

$=-\frac{\pi }{3}$

$\Rightarrow$ Statement II is not true.

Hence, option A is correct.