Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2021MathematicsComplex NumberActual

If i= -1 , then how many values does i^ -2 n have for different n Z ?

Options

  1. AOne
  2. BTwo
  3. CFour
  4. DInfinite

Correct answer

B. Two

Step-by-step solution

aligned & i^ -2 n = 1 i^ 2 n = ( 1 i^2 )^n=(-1)^n & i^ -2 n = array l 1 when n is even -1 when n is odd array . aligned

Practice Complex Number on Quantrex Academy →

More from Complex Number

Consider the following inequalities : I. 1+4i>3+2i II. 2+3i III. 4+3i>3+4i where i= -1 How many of the above are valid ? 2026If p , q , r are the cube roots of unity, then what is vmatrix p^2+q^2 & r^2 & r^2 p^2 & q^2+r^2 & p^2 q^2 & q^2 & r^2+p^2 vmatrix equal to ? 2026If , , are cube roots of -8 , then what is ^2 p^2+ ^2 q^2+ ^2 r^2 ^2 p^2+ ^2 q^2+ ^2 r^2 equal to ? 2026Let Z₁ and Z₂ be complex numbers such that 3Z₁ 4Z₂ is purely imaginary. What is | Z₁+Z₂ Z₁-Z₂ | equal to ? 2026If is a non-real cube root of unity, then what is a root of the following equation? vmatrix x+1 & & ^2 & x+ ^2 & 1 ^2 & 1 & x+ vmatrix = 0 2025If x + 1 x = 2 , then what is x^3 + 1 x^3 equal to? 2025If z 0 is a complex number, then what is amp (z) + amp ( z ) equal to? 2025If = -1 + -3 2 , then what is the value of (1 + ¹⁹ - ³⁵)¹⁰⁰ - (1 - 3 ²⁵ + ³⁸)⁵⁰ ? 2025 Full Complex Number list All NDA PYQs