Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201911 Jan 2019Evening ShiftMathematicsComplex NumberActual

Let z be a complex number such that |z|+z=3+i( where i= -1 ) Then | z | is equal to :

Options

  1. A34 3
  2. B5 3
  3. C41 4
  4. D5 4

Correct answer

B. 5 3

Step-by-step solution

Since, |z|+z=3+i Let z=a+i b, then |z|+z=3+i a²+b² +a+i b=3+i Compare real and imaginary coefficients on both sides array l b=1, a²+b² +a=3 a²+1 =3-a a²+1=a²+9-6 a 6 a=8 a= 4 3 array Then, |z|= ( 4 3 )²+1 = 16 9 +1 = 5 3

Practice Complex Number on Quantrex Academy →

More from Complex Number

The number of values of z C , satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5 , is: 2026Let S = z C : z^2 + 6 ,iz - 3 = 0 . Then _ z S z^8 is equal to : 2026Let the set of all values of k R such that the equation z( z + 2 + i) + k(2 + 3i) = 0 , z C , has at least one solution, be the interval [ , ] . Then 9( + ) is equal to: 2026Let z₁, z₂ C be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 . Then |z₁|^2 + |z₂|^2 is equal to : 2026Let S= z C : z^2+4z+16=0 . Then _ z S |z+ 3 i|^2 is equal to: 2026Let z be a complex number such that |z+2| = |z-2| and ( z+3 z-i ) = 4 . Then |z|^2 is equal to: 2026Let the circles C₁ : |z| = r and C₂ : |z - 3 - 4i| = 5 , z C , be such that C₂ lies within C₁ . If z₁ moves on C₁ , z₂ moves on C₂ and |z₁ - z₂| = 2 , then |z₁ - z₂| is equal to: 2026Let x and y be real numbers such that 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i , i = -1 . Then the value of 10(x - 3y) is : 2026 Full Complex Number list All JEE Main PYQs