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Express the following expression in the ...

Express the following expression in the form of `a + i b``((3+isqrt(5))(3-isqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-isqrt(2)))`

A

`4+i(-(7 sqrt(2))/(2))`

B

`0+i(-(7 sqrt(6))/(2))`

C

`0+i(-(14 sqrt(2))/(2))`

D

`0+i(-(7 sqrt(2))/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Given expression
`" "((3+isqrt(5))(3-isqrt(5)))/((sqrt(3)+sqrt(2)i)- (sqrt(3)-isqrt(2)))`
`" "((3)^(2)-(isqrt(5))^(2))/(sqrt(3)+sqrt(2)i-sqrt(3)+isqrt(2))=(9-5i^(2))/(2 sqrt(2)i)`
`" "=(9-5(-1))/(2sqrt(2)i)=(9+5)/(2sqrt(2)i)=(14)/(2sqrt(2)i)`
`" "=(7)/(sqrt(2)i)=(7)/(sqrt(2)i)xx(i)/(i)=(7i)/(sqrt(2)i^(2))`
`" "=-(7)/(sqrt(2))xx(sqrt(2))/(sqrt(2))i=-(7sqrt(2))/(2)i`
`" "=0+i(-(7 sqrt(2))/(2))`
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