Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2023Morning ShiftMathematicsComplex NumberActual

If i= -1 and n is a positive integer, then i^n+i^ n+1 +i^ n+2 +i^ n+3 is equal to

Options

  1. Ai^n
  2. B0
  3. C1
  4. Di

Correct answer

B. 0

Step-by-step solution

The expression is i^n + i^ n+1 + i^ n+2 + i^ n+3 . Factoring out i^n , we get i^n(1 + i + i^2 + i^3) . Since i^2 = -1 and i^3 = -i , the expression becomes i^n(1 + i - 1 - i) . Simplifying the terms inside the parentheses: 1 - 1 + i - i = 0 . Therefore, i^n(0) = 0 . Answer: 0

Practice Complex Number on Quantrex Academy →

More from Complex Number

If z and are two non-zero complex numbers such that |z |=1 and Arg z- Arg = 2 then z = 2025Let z satisfy |z|=1, z=1- z and Im (z)>0 Statement-I : z is a real number Statement-II : Principal argument of z is 3 . Then 2025If ₁ and ₂ are two non-zero complex numbers and a , b are non zero real numbers such that | a ₁+ b ₂ |= | a ₁- b ₂ | , then ₁ ₂ is 2025If a complex number z=x+i y represents a point P on the Argand plane and Arg ( z-3+2 i z+2-3 i )= 4 , then the locus of P is a 2025By taking a i b =x i y, x>0 , if we get 21+12 2 i 21-12 2 i =a+i b , then b a = 2025Two values of (-8-8 3 i)^ 1 / 4 are 2025If x=3-2 3 i , then x^4-12 x^3+54 x^2-108 x-54= 2025z ₁, z ₂, z ₃ represent the vertices A , B , C of a triangle ABC respectively in the Argand plane. If |z₁-z₂ |= 25-12 3 , | z₁-z₃ z₂-z₃ |= 3 4 and ACB =30^ , then the area (in sq. 2025 Full Complex Number list All COMEDK PYQs