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If z = x + iy is a complex number such that |z + 2| = |z – 2|, then the locus of z is _____ 

(a) real axis

(b) imaginary axis 

(c) ellipse 

(d) circle

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(b) imaginary axis

|z + 2| = | z – 2| 

⇒ |x + iy + 2| = |x + iy – 2| 

⇒ |x + 2 + iy|2 = |x – 2 + iy|2

⇒ (x + 2)2 + y2 = (x – 2)2 + y2 

⇒ x2 + 4 + 4x = x2 + 4 – 4x 

⇒ 8x = 0 

⇒ x = 0

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