Zaymiey

📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

i¹⁰⁰ =

Answer: 1.

  • A i
  • B -i
  • C 1
  • D -1

Correct answer: C. 1

Explanation: Powers of i cycle with period 4. 100 = 4 x 25, remainder 0. i<sup>100</sup> = (i<sup>4</sup>)<sup>25</sup> = 1<sup>25</sup> = 1.

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 →