Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2024MathematicsComplex NumberActual

Let S= a+b 2 : a, b Z , T₁= (-1+ 2 )^n: n N , and T₂= (1+ 2 )^n: n N . Then which of the following statements is (are) TRUE?

Options

  1. AZ T₁ T₂ S
  2. BT₁ (0, 1 2024 )= , where denotes the empty set.
  3. CT₂ (2024, )
  4. DFor any given a, b Z , ( (a+b 2 ))+i ( (a+b 2 )) Z if and only if b=0 , where i= -1 .

Correct answer

A. Z T₁ T₂ S

Step-by-step solution

(1) aligned & (-1+ 2 )^ n = m + 2 n , m , where, n Z & (1+ 2 )^ n = m ₁+ 2 n ₁, where, ~m ₁, n ₁ Z & Z T ₁ T ₂ S aligned but b 2 S for negative b Z . So Z T ₁ T ₂ S (2) aligned & ( 2 -1)^ n = 1 ( 2 +1)^ n 2024, where, n N & T ₂ (2024, ) aligned (4) ( (a+b 2 )=0) b=0, where, a Z Options (1), (3), (4) are Correct.

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 Advanced PYQs