findthe values of 'x' and 'y' for which the complex numbers -3+ix2y and x2+y+4i are conjugate of each other - Maths - Complex Numbers and Quadratic Equations

Question

findthe values of 'x' and 'y' for which the complex numbers
-3+ix2y and x2+y+4i are conjugate of each
other

Priyanka Kedia · Accepted Answer

Given,the complex number -3+ix2y and x2+y+4i are conjugate of each other
 So,-3+ix2y= x2+y+4i¯⇒-3+ix2y=x2+y-4iEquating real and imaginary part on both side, we have,x2+y=-3⇒y=-3-x2      
1   and, x2y=-4          
2Sbstitute value of y from equation 1 in equation 2, x2-3-x2=-4⇒-3x2-x4+4=0⇒x2-1x2+4=0⇒x2=1   or x2=-4discard this value because x is a real number⇒x=±1Substitute x=±1 in equation1,y=-3-±12=-3-1=-4Thus, x=±1 and y=-4