for every value of c =0,find all the complex numbers z which satisfy the equation |z|2-2iz+2c(1+i)=0 - Maths - Complex Numbers and Quadratic Equations

Question

for every value of c =0,find all the complex numbers z which
satisfy the equation |z|2-2iz+2c(1+i)=0

Priyanka Kedia · Accepted Answer

Let z=x+iy, so the given equation
becomes,x2+y2-2ix+2y+2c+2ic=0⇒x2+y2+2y+2c-i2x-2c=0-i0Comparing
real and imaginary part, we
have,2x-2c=0⇒x=cAnd,x2+y2+2y+2c=0⇒y2+2y+2c+c2=0For real
value of y, discriminant will be positive i e
,4-42c+c2≥0⇒c2+2c-1≤0⇒c+2+1c-2-1≤0⇒0≤c≤2-1For,
c=0, y=0,-2So, z=0 , -2i

for every value of c =0,find all the complex numbers z which satisfy the equation |z|2-2iz+2c(1+i)=0.

for every value of c =0,find all the complex numbers z which satisfy the equation |z|²-2iz+2c(1+i)=0.