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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z = √3 + i, what is |z| and arg(z)?

Answer: |z|=2, arg=π/6.

  • A |z|=2, arg=π/6
  • B |z|=2, arg=π/3
  • C |z|=√2, arg=π/4
  • D |z|=4, arg=π/6

Correct answer: A. |z|=2, arg=π/6

Explanation: |z| = sqrt(3+1) = 2. arg(z) = tan<sup>-1</sup>(1/sqrt(3)) = pi/6.

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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