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

Question

The complex number ((-√3+3i) (1-i)/(3+√3i)(i)(√3+√3i)) when represented in the Argand diagram lies (A) on the X-axis (Real axis) (B) on the Y-axis (Imaginary axis) (C) in the first quadrant (D) in the second quadrant

Tardigrade Admin · Accepted Answer

Let z=((-√3+3 i)(1-i)/(3+√3 i) i(√3+√3 i)) =(1/√3)((1-i/1+i) × (1-i/1-i)) =(1/√3)((1-1-2 i/1+1)) =-(i/√3) The complex number z is represented on y -axis (imaginary axis).

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

on the X-axis (Real axis)

on the Y-axis (Imaginary axis)

in the first quadrant

in the second quadrant

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

Q. The complex number (3+3i​)(i)(3​+3i​)(−3​+3i)(1−i)​ when represented in the Argand diagram lies