Express the following expression in the form (a+ib), `frac{(3+i sqrt 5)(3-i sqrt 5)}{(sqrt 3 + sqrt 2 i) - (sqrt 3 - sqrt 2 i)}`

Simplify the following and express in the form (a+ib): frac{sqrt 5 +sqrt 3 i}{sqrt 5 - sqrt 3 i}

Expand: (i) (sqrt 3 + sqrt 2)^4 (ii) (sqrt 5 - sqrt 2)^5

Answer the following. Simplify the following and express in the form a + ib: (sqrt(5) + sqrt(3i)) / (sqrt(5) - sqrt(3i))

Express the following in the form of (a+ib), a,b in R, i= sqrt (-1) State the values of a and b: ( sqrt 5 +2 sqrt (-4) )+(1- sqrt (-9) )+(2+3i)(2-3i)

Express the following in theform a+ib, a, b in R, using De-Moiver's theorem: (-2sqrt 3-2i)^5

Express the following in the form of (a+ib), a,b in R, i= sqrt (-1) State the values of a and b: (1+i)^(-3)

Simplify the following and express in the form (a+ib): frac{5+7i}{4+3i} + frac{5+7i}{4-3i}

Express the following in the modulus amplitude form (polar form). 1 + sqrt(3) i