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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

For z₁ = 1 + i and z₂ = 1 - i, find z₁/z₂.

Answer: i.

  • A -i
  • B 1
  • C 2i
  • D i

Correct answer: D. i

Explanation: z<sub>1</sub>/z<sub>2</sub> = (1+i)/(1-i). Multiply by (1+i)/(1+i): (1+i)<sup>2</sup>/2 = 2i/2 = i.

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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