Zaymiey

📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The polar form of z = -i is:

Answer: cos(-90°) + i sin(-90°).

  • A 1(cos 90° + i sin 90°)
  • B 1(cos 270° + i sin 270°)
  • C 1(cos 180° + i sin 180°)
  • D cos(-90°) + i sin(-90°)

Correct answer: D. cos(-90°) + i sin(-90°)

Explanation: z = -i = 0 - 1i. Modulus = 1, arg = -pi/2 = -90 degrees. Polar: cos(-90) + i sin(-90).

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

Read the full Complex Numbers and Quadratic Equations notes →