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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The value of i⁻³⁵ is:

Answer: i.

  • A i
  • B -i
  • C 1
  • D -1

Correct answer: A. i

Explanation: i⁻³⁵=1/i³⁵. Find i³⁵: 35=4×8+3, so i³⁵=(i⁴)⁸·i³=1⁸·(-i)=-i. Thus i⁻³⁵=1/(-i). Rationalize: multiply by i/i: i/(-i²)=i/(-(-1))=i/1=i. Answer: i⁻³⁵ = 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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