Question

Find the sqare root of i (complex numbers)

Answer 1

X² = i         as  X = √i   and     i = √-1

Let us assume  X = A + B i
So, (A+i B)² = i
A² + i² B² + 2 AB i = i
(A²-B²) = 0      2 AB = 1
A = +- B      So  2 A² = 1/2        A = B = +1/√2  or -1/√2

X =  (1+i) /√2   or  -(1+i) / √2

Answer 2

i=√(-1)  since,i²=-1 
(a+/-ib)²=i
a²+i²b²+2abi=i
a²-b²=0  and  2ab=1
a=-+b  
therefore sq roots are i+1/√2   and -(1+i)/√2.