Question

Expression $\frac{4}{1+\sqrt{3}i}+\frac{4}{1-\sqrt{3}i}$ is

• A. a rational number but not integer
• B. an irrational number
• C. a purely imaginary number
• D. an integer
  

Answer 1

Answer: (D)

an integer

Given, $\frac{4}{1+\sqrt{3}i}+\frac{4}{1-\sqrt{3}i}$

$=\frac{4}{1+\sqrt{3}i}\left(\frac{1-\sqrt{3}i}{1-\sqrt{3}i}\right)+\frac{4}{1-\sqrt{3}i}\left(\frac{1+\sqrt{3}i}{1+\sqrt{3}i}\right)$

$=(1-\sqrt{3}i)+(1+\sqrt{3}i)=2$
is an integer.
Hence, option D.