If z₁= 3 +i 3 and z₂= 3 +i , then the complex number ( z ₁ z ₂ )⁵⁰ lies in the :

Step-by-step solution

( z₁ z₂ )⁵⁰= ( 3 +i 3 3 +i )⁵⁰= [ ( 3 (1+i) 3 +i )² ]²⁵= [ 3(2 i) 3-1+2 3 i ]²⁵= ( 3 i 1+ 3 i )²⁵= 3²⁵ i²⁵ (-2 ² )²⁵ array l =-i . ( 3 2 )²⁵=- i ( -1+ 3 i 2 ) ( 3 2 )²⁵ = ( 3 2 )²⁵ ( 3 2 + 1 2 i ) array Hence, ( z₁ z₂ )⁵⁰ lies in the first quadrant as both real and imaginary parts of this number are positive.