If `(sqrt(8)+i)^(50)=3^(49)(a+i b)` , then find the value of `a^2+b^2dot`

If log_(sqrt8) b = 3 1/3 , then find the value of b.

If A-B=30^(@)andsinA=(sqrt(3))/(2) ,then find the value of B.

" If "(i^(4)+i^(9)+i^(16))/(2-i^(8)+i^(10)+i^(3))=a+ib," then find the value of "a" and "b

If a=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and b=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) , then find the value of 3(a^(2)-b^(2)) .

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

If (a+ib)=i^(i-oo), find the value of a^(2)+b^(2) and (b)/(a).