Complex NumbersMedium

Question

The complex numbers z = x + iy which satisfy the equation = l, lie on

Options

A.the x-axis
B.the straight line y = 5
C.a circle passing through the origin
D.None of the above

Solution

      
Given, = 1
⇒     |z - 5i| = |z + 5i|
(if |z - z1| = | z + z2|, theb it is a perpendicular bisector of z1 and z2 )
∴ Perpendicular bisector of (0 , 5) and (0, - 5) is x-axis.

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