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  4. The complex number ((-√3+3i) (1-i)/(3+√3i)(i)(√3+√3i)) when represented in the Argand diagram lies

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Q. The complex number $\frac {(-\sqrt3+3i) (1-i)}{(3+\sqrt{3i})(i)(\sqrt{3}+\sqrt{3i})}$ when represented in the Argand diagram lies

KCETKCET 2006Complex Numbers and Quadratic Equations

Solution:

Let $z=\frac{(-\sqrt{3}+3 i)(1-i)}{(3+\sqrt{3} i) i(\sqrt{3}+\sqrt{3} i)}$
$=\frac{1}{\sqrt{3}}\left(\frac{1-i}{1+i} \times \frac{1-i}{1-i}\right) $
$=\frac{1}{\sqrt{3}}\left(\frac{1-1-2 i}{1+1}\right) $
$=-\frac{i}{\sqrt{3}}$
The complex number $z$ is represented on $y$ -axis (imaginary axis).