Q. The complex number $\frac{\left( - \sqrt{3} + 3i \right)(1 - i)}{\left( 3 + \sqrt{3}i \right)(i)(\sqrt{3} + \sqrt{3}i)}$ when represented in the Argand daigram is
A) In the second quadrant
B) In the first quadrant
C) On the $y$-axis (imaginary axis)
D) On the $x$-axis (real axis)
Explanation
(c)
Let $z = \frac{\left( - \sqrt{3} + 3i \right)(1 - i)}{\left( 3i - \sqrt{3} \right)\sqrt{3}(1 + i)}$
$= \frac{1}{\sqrt{3}}\left( \frac{1 - i}{1 + i} \times \frac{1 - i}{1 - i} \right) = - \frac{i}{\sqrt{3}}$
The complex number $z$ is represented on $y$-axis (imaginary axis)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.