A) in the second quadrant
B) in the first quadrant
C) on the y-axis (imaginary axis)
D) on the x-axis (real axis).
Correct Answer: C
Solution :
Let \[z=\frac{(-\sqrt{3}+3i)\,(1-i)}{(3+\sqrt{3}i)\,i\,(\sqrt{3}+\sqrt{3}i)}\] \[=\frac{(-\sqrt{3}+3i)(1-i)}{(3i-\sqrt{3})\,\sqrt{3}\,(1+i)}\] \[=\frac{1}{\sqrt{3}}\left( \frac{1-i}{1+i}\times \frac{1-i}{1-i} \right)\] \[=\frac{1}{\sqrt{3}}\left( \frac{1-1-2i}{1+1} \right)\] \[=-\frac{i}{\sqrt{3}}\] The complex number z is represented on y-axis (imaginary axis).
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