Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20226 Aug 2022Morning ShiftMathematicsComplex NumberActual

If (x+i y)^ 1 / 3 =a+i b where x, y, a, b R and i= -1 , then x a - y b =

Options

  1. A-2 (a^2+b^2 )
  2. B2 (a^2-b^2 )
  3. Ca^2-b^2
  4. Da^2+b^2

Correct answer

A. -2 (a^2+b^2 )

Step-by-step solution

aligned & (x+i y)^ 1 / 3 =a+i b x+i y=(a+i b)^3= (a^3-3 a b^2 )+i (3 a^2 b-b^3 ) & x a =a^2-3 b^2 and y b =3 a^2-b^2 & x a - y b =-2 (a^2+b^2 ) 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