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Find the multiplicative inverse of the complex number `sqrt(5)+3i`

A

`(sqrt(6))/(14)-(3)/(14)i`

B

`(sqrt(2))/(14)-(1)/(14)i`

C

`(sqrt(3))/(14)-(1)/(14)i`

D

`(sqrt(5))/(14)-(3)/(14)i`

Text Solution

Verified by Experts

The correct Answer is:
D
Multiplicative inverse of `sqrt(5)+3i`
`" "=(1)/(sqrt(5)+3i)=(1)/(sqrt(5)+3i)xx(sqrt(5)- 3i)/(sqrt(5)-3i)`
`" "=(sqrt(5)-3i)/((sqrt(5))^(2)-(3i)^(2))=(sqrt(5)-3i)/(5-9i^(2))`
`" "= (sqrt(5)-3i)/(5-9xx(-1))=(sqrt(5)- 3i)/(14)`
`" "=(sqrt(5))/(14)-(3)/(14)i`
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