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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z = 2(cos 60° + i sin 60°), find z in a+ib form.

Answer: 1 + √3i.

  • A 2 + 2i
  • B √3 + i
  • C 1 + i
  • D 1 + √3i

Correct answer: D. 1 + √3i

Explanation: z = 2(1/2 + i sqrt(3)/2) = 1 + sqrt(3) 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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