Question

kindly help me in solving the problem​

Answer 1

(i) ( √-4 ) ^17

=> √ -4 = √ 4 × √ -1 = 2i

=> ( 2i ) ^17

=> 2 ^17 × i ^17

=> 2 ^17 × (i⁴)⁴ × i

since , i⁴ = 1

therefore , ( √-4 ) ^17 = 2 ^17 i

ii) ( √-5 )^5

=> √-5 = √5 × √-1 = √5 i

=> ( √5i ) ^5 = 25√5 × i ^5

as , i⁴ = 1 => i ^5 = i

therefore,

=> ( √-5 ) ^5 = 25√5 i