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If sqrt(a+i b)=x+i y ,\ then possible ...

If `sqrt(a+i b)=x+i y ,\ `
then possible value of `sqrt(a-i b)` is
a. `x^2+y^2`
b. `sqrt(x^2+y^2)`
c. `x+i y`
d. `x-i y`
e. `sqrt(x^2-y^2)`

Text Solution

Verified by Experts

D)`(sqrt{a+i b}=x+i y)`
`(Rightarrow a+i b=(x+i y)^{2}=x^{2}-y^{2}+2 i x y)`
`(Rightarrow a=x^{2}-y^{2}, b=2 x y)`
`(a-i b=x^{2}-y^{2}-2 i x y)`
`(=x^{2}+(i y)^{2}-2 i x y)`
`(a-i b=(x-i y)^{2})`
`(therefore sqrt{a-i b}=x-i y)`
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