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Question
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
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Solution
`((3 + isqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
= `((3)^2 - (isqrt5)^2)/(sqrt3 + sqrt2i - sqrt3 + sqrt2i` `[(a+b) (a +b) = a^2 - b^2]`
= `(9 - 5i)^2/(2 sqrt2i)`
= `(9 - 5 (-1))/(2 sqrt2i)` `[i^2 = -1]`
= `(9 + 5)/(2 sqrt2i) xx i/i`
= `(14i)/((2sqrt2) (-1))`
= - `(7i)/sqrt2 xx sqrt2/sqrt2`
= `(-7 sqrt2i)/2`
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