Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202120 Sep 2021Morning ShiftMathematicsComplex NumberActual

The value of (1+i)^5(1-i)^7

Options

  1. A-64
  2. B-64 i
  3. C64 i
  4. D64

Correct answer

B. -64 i

Step-by-step solution

aligned & (1+i)^5(1-i)^7 = & (1+i)^5(1-i)^5(1-i)^2=[(1+i)(1+i)(1-i)]^5 (1-2 i+i^2 ) = & (1-i^2 )^5(-2 i)=(2)^5(-2 i)=-64 i [ i^2=-1 ] 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 MHT CET PYQs