निम्नलिखित व्यंजको को `a + ib` के रूप में व्यक्त कीजिए:
(i) `((3 + i sqrt5) (3- i sqrt5))/((sqrt3 + sqrt2i) - (sqrt3 - i sqrt2))` (ii) `(5 -3i)^(3)`

Explanation

(i) `((3 + isqrt5) (3 - i sqrt5))/((sqrt3 + sqrt2i) - (sqrt3 - i sqrt2)) = ((3)^(2) - (i sqrt5)^(2))/(sqrt3 + sqrt2i - sqrt3 + i sqrt2)`
`(9 - 5i^(2))/(2 sqrt2i) = (9 + 5)/(2 sqrt2) = (14)/(2 sqrt2i) = (7)/(sqrt2i)`
`= (7)/(sqrt2i) xx (sqrt2i)/(sqrt2i)`
`= (7 sqrt2i)/(2i^(2)) = (-7 sqrti)/(2)`
(ii) `(5 -3i)^(3) = (5)^(3) - 3(5)^(2) (3i) + 3(5) (3i)^(2) - (3i)^(3)`
`= 125 - 225i + 35i^(2) - 27i^(3)`
`= 125 - 225i - 135 - 27i^(2).i`
`= -10 - 225i + 27i`
`= -10 - 198i`