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

The smallest positive integer n for which ( 1-i 1+i )^ n^2 where i= -1 , is

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

A. 2

Step-by-step solution

aligned & ( 1-i 1+i )^ n^2 =1 & ( (1-i)(1-i) (1+i)(1-i) )^ n^2 =1 aligned aligned & ( (1)^2+(i)^2-2 i 1-(i)^2 )^ n^2 =1 & ( -2 i 2 )^ n^2 =1 (-i)^ n^2 =1 aligned For n=2,(-i)^ 2^2 =(-i)^4=1 Hence, n=2 .

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