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The complex number, z=((-sqrt(3)+3i)(1-i...

The complex number, `z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))`

A

lies on real axis

B

lies on imaginary axis

C

lies in first quadrant

D

lies in second quadrant

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))`
`=(sqrt(3)(-1+sqrt(3)i)(1-i))/(3(sqrt(3)+i)(i)(1+i))`
`=((-1+sqrt(3)i)(1-i))/(sqrt(3)(-1+sqrt(3)i)(1+i))`
`=((1-i)^(2))/(2sqrt(3))=(-2i)/(2sqrt(3))`, which lies on imaginergy axis
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