For what values of x and y are the nos 3+ix2y and x2+y+4i conjugate complexes - Maths - Complex Numbers and Quadratic Equations

Question

For what values of x and y are the nos 3+ix2y and
x2+y+4i conjugate complexes?

Ajanta Trivedi · Accepted Answer

Complex conjugate of 3+i x2y is 3-i
x2y where x and y are real
It is given that complex conjugate of 3+i x2y is x2+y+i 4
therefore,
3-i x2y=x2+y+i 4
comparing the real and imaginary parts, we have:

x2+y=3 (1) x2y=-4 (2)⇒y=-4x2now, from 1, we
getx2-4x2=3x4-3x2-4=0x4-4x2+x2-4=0x2(x2-4)+1(x2-4)=0(x2-4)(x2+1)=0x2-4=0
or x2+1=0⇒x2=4 or x2=-1Rejected

⇒x=±2 since x is a real number

therefore 2 and -2 are two values of x and

y=-4x2=-44=-1

hope this helps you

For what values of x and y are the nos 3+ix2y and x2+y+4i conjugate complexes?

For what values of x and y are the nos 3+ix²y and x²+y+4i conjugate complexes?