Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202022 Sep 2020Morning ShiftMathematicsComplex NumberActual

The modulus of the complex number ( 2+i 5 2-i 5 )¹⁰+ ( 2-i 5 2+i 5 )¹⁰ is

Options

  1. A2 (20 ⁻¹ ( 2 3 ) )
  2. B2 (10 ⁻¹ ( 2 3 ) )
  3. C2 (10 ⁻¹ ( 2 3 ) )
  4. D2 (20 ⁻¹ ( 2 3 ) )

Correct answer

A. 2 (20 ⁻¹ ( 2 3 ) )

Step-by-step solution

Given complex number Z= ( 2+i 5 2-i 5 )¹⁰+ ( 2-i 5 2+i 5 )¹⁰ Let 2=r and 5 =r r=3 Then, z= ( +i -i )¹⁰+ ( -i +i )¹⁰ aligned & = (20 )+i (20 )+ (20 )-i (20 ) & =2 20 & |Z|=2| 20 |=2 (20 ⁻¹ ( 2 3 ) ) aligned

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 AP EAMCET PYQs