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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z = x + iy and |z - 1| + |z + 1| = 4, the locus is:

Answer: Ellipse.

  • A Circle
  • B Ellipse
  • C Parabola
  • D Hyperbola

Correct answer: B. Ellipse

Explanation: |z-1| + |z+1| = sum of distances from (x,y) to (1,0) and (-1,0) = 4 (constant). This is an ellipse with foci at (pm1, 0).

Argand Plane: z = a + ibReImz = a+iba (real part)b (imaginary part)θ = arg(z)|z| = length of the vector OZ = √(a²+b²); θ = angle OZ makes with the positive real axis

A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.

Concept context

Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots

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