For any two complex numbers z, and z2, prove thatRe (, z) = Reg Re z2- – InterviewSolution

1.

For any two complex numbers z, and z2, prove thatRe (, z) = Reg Re z2-1mzi Ä°mz2.

Answer»

let z1 = x+iy and z2 = u + iv Rez1*Rez2 - Imz1*Imz2 = xu-vy

now z1z2 = (x+iy)(u+iv) = xu + ixv + iuy + i²vy = (xu-vy) + i(xv-uy)

so, Re(z1z2) = (xu-vy)

=> L.H.S = R.H.S

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