`((5+sqrt(2)i))/((1-sqrt(2)i))`

Express the following in the form a + i b (i) (5+sqrt(2i))/(1-sqrt(2i)) (ii) i^(-35)

((1+i)/(sqrt(2)))^8+((1-i)/(sqrt(2)))^8 is equal to

Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))^2)/(-2i(-sqrt(3)+i))

Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))^2)/(-2i(-sqrt(3)+i))

Simplify: (i)\ ((sqrt(2))/5)^8\ -:((sqrt(2))/5)^(13)

Rationalies the denominator and simplify: (i) (1+sqrt(2))/(3-2sqrt(2)) (ii) (2sqrt(6)-\ sqrt(5))/(3sqrt(5)-\ 2sqrt(6))

Simiplify : (sqrt((5+12i)) + sqrt((5-12i)))/(sqrt((5+12i))-sqrt((5-12i)))

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)

Express the following complex number in the polar form: (2+6sqrt(3)i)/(5+sqrt(3)i)