Let S = {z = x + iy : frac{2z - 3i}{4z + 2i} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $z = x + iy$. The expression is $\frac{2(x + iy) - 3i}{4(x + iy) + 2i} = \frac{2x + i(2y - 3)}{4x + i(4y + 2)}$.For a complex number $\frac{a

Vedclass · Accepted Answer

$(x, y) = (0, -\frac{1}{2})$

Vedclass · Answer

(C) Let $z = x + iy$. The expression is $\frac{2(x + iy) - 3i}{4(x + iy) + 2i} = \frac{2x + i(2y - 3)}{4x + i(4y + 2)}$.For a complex number $\frac{a + ib}{c + id}$ to be real,the imaginary part of the product $\frac{a + ib}{c + id} 	imes (c - id)$ must be zero.This implies $ad - bc = 0$,or $\frac{a}{c} = \frac{b}{d}$.Here,$a = 2x$,$b = 2y - 3$,$c = 4x$,$d = 4y + 2$.Setting the imaginary part of the numerator of the product to zero: $2x(4y + 2) - 4x(2y - 3) = 0$.$8xy + 4x - 8xy + 12x = 0 \implies 16x = 0 \implies x = 0$.Also,the denominator $4z + 2i 
eq 0$,so $4(x + iy) + 2i 
eq 0 \implies 4x + i(4y + 2) 
eq 0$.Since $x = 0$,we must have $4y + 2 
eq 0$,so $y 
eq -\frac{1}{2}$.Thus,the set $S$ consists of points $(0, y)$ where $y 
eq -\frac{1}{2}$.Option $C$ states $(x, y) = (0, -\frac{1}{2})$,which is excluded from $S$. Therefore,$C$ is $NOT$ correct.

Let $S = \{z = x + iy : \frac{2z - 3i}{4z + 2i} \text{ is a real number} \}$. Then which of the following is $NOT$ correct?

Similar Questions

$P$ is a point denoting $z$ in the Argand diagram. If $\frac{z-i}{z-1}$ is always purely imaginary,then the locus of $P$ is

The points in the Argand plane represented by the complex conjugates of $1+2i, 2-3i, 3-4i$:

If $a = \cos \alpha + i\sin \alpha$,$b = \cos \beta + i\sin \beta$,$c = \cos \gamma + i\sin \gamma$ and $\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 1$,then $\cos (\beta - \gamma ) + \cos (\gamma - \alpha ) + \cos (\alpha - \beta )$ is equal to

The points $z_1, z_2, z_3, z_4$ in the complex plane are the vertices of a parallelogram taken in order,if and only if

If three complex numbers are in $A.P.$,then they lie on

Vedclass Test Series

Exam Paper Generator

Online Exam Module