Let C be the set of complex numbers. Prove that the mapping `F:C to R` given by `f(z)=|z|, AA z in C,` is neither one-one nor onto.

Answer

N/a

Explanation

The mapping ` " " f: C to R`
Given, `f(z)=|z|,AA z in C`
`f(1)=|1|=1`
`f(-1)=|-1|=1`
`f(1)=f(-1)`
But `1 ne -1`
So, f(z) is not one-one. Also, f(z) is not onto as there is no pre-image for any negative element of R under the mapping f(z).