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Mathematics Question on types of differential equations

Let s={z=x+ry:2z−3i4z+2iz=x+ry:\frac{2z-3i}{4z+2i} is a real number}. Then which of the following is not correct?

A

x=0

B

y∈(−∞,−12)∪(−12,−∞)y∈(-∞,-\frac{1}{2})∪(-\frac{1}{2},-∞)

C

y+x2+y2≠−14y+x^2+y^2 ≠-\frac{1}{4}

D

(x,y)=(0,12)(x,y)=(0,\frac{1}{2})

Answer

y∈(−∞,−12)∪(−12,−∞)y∈(-∞,-\frac{1}{2})∪(-\frac{1}{2},-∞)

Explanation

Solution

The correct option is(B): y∈(−∞,−12)∪(−12,−∞)y∈(-∞,-\frac{1}{2})∪(-\frac{1}{2},-∞)