If is a complex number such that ²- +1=0 , then ²⁰¹¹ is equal to

Step-by-step solution

Given, ²- +1=0 = -(-1) (-1)²-4(1)(1) 2 1 = 1 1-4 2 = 1 -3 2 = 1 3 i 2 =- ,- ² ²⁰¹¹=(- )²⁰¹¹=(-1)²⁰¹¹ ²⁰¹¹=(-1) ( ³ )⁶⁷⁰ =(-1)(1)⁶⁷⁰ =- = ( ³=1 ) If we take =- ² aligned ²⁰¹¹ &= (- ² )²⁰¹¹=- ( ²⁰¹¹ )² &=- [ ( ³ )⁶⁷⁰ ]² &=-( )² &=- ²= aligned Hence, in both cases ²⁰¹¹=