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प्रश्न
Obtain the Cartesian form of the locus of z = x + iy in the following cases:
|z + i| = |z – 1|
उत्तर
z = x + iy
|z + i| = |z – 1|
⇒ |x + iy + i| = | x + iy – 1|
⇒ |x + i(y + 1)| = |(x – 1) + iy|
Squaring on both sides
|x + i(y + 1)|2 = |(x – 1) + iy|2
⇒ x2 + (y + 1)2 = (x – 1)2 + y2
⇒ x2 + y2 + 2y + 1 = x2 – 2x + 1 + y2
⇒ 2y + 2x = 0
⇒ x + y = 0
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