Determine the real part of the complex number z that statisfies the equation 4Z + 1 Y = 10 + 12i, where Y is the conjugate of Z.

• let z=a+ib .So y=a-ib(because of y is conjugate of z).putting the value of y and z in equation-
  4*(a+ib)+1*(a-ib)=10+12i. By comparing real and imaginary part of both sides we got->a=2 and b=4
  So...z=2+4i
  hence real part of complex no. z is->2(ans)
  
• 9 years agoHelpfull: Yes(20) No(0)
• consider z=x+iw and if y iz conjugate of z then it will be y=x-iw. put into the equation
  4*(x+iw)+1*(x-iw)=10+12i
  5x+4iw=10+12i.. comparing both x=2 ,w=3... then z=2+3i and y=2-3i (ans)
• 9 years agoHelpfull: Yes(10) No(11)
• we can write z=(x+iy)
  so the given exp. 4z+1y is equals
  4*(x+iy)+1*(x+iy)=(4x+4iy+x-iy)=(5x+3iy)
  compare the L.H.S and R.H.S
  5x+3iy = 10 + 12i
  5x=10
  =>x=2.
  3y=12
  =>y=4
• 9 years agoHelpfull: Yes(4) No(1)
• let the complex number Z be x+iy so conjugate Y be x-iy.
  so,4(x+iy)+1(x-iy)=10+12i
  on solving and equating we get 4+3i as z
  so real part of z is 4
• 9 years agoHelpfull: Yes(1) No(5)
• real part of z is 2
• 9 years agoHelpfull: Yes(0) No(0)