Let z be a complex number such that |z+2| = |z-2| and ( z+3 z-i ) = 4 . Then |z|^2 is equal to:

Step-by-step solution

Given |z+2| = |z-2| , the point z lies on the perpendicular bisector of the line segment joining (-2, 0) and (2, 0) . This means z lies on the imaginary axis. Let z = iy , where y R . We are given ( z+3 z-i ) = 4 . Substituting z = iy , we get: iy+3 iy-i = 3+iy i(y-1) = -i(3+iy) y-1 = y - 3i y-1 = y y-1 - i 3 y-1 For a complex number X + iY to have an argument of 4 , its real and imaginary parts must be equal and strictly positive. Therefore: y y-1 = -3 y-1 > 0 Since y 1 , equating the numerators gives y = -3 . Che