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Let C be the set of complex numbers. Pro...

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.

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Given ,
`f(z)=∣z∣` for all `Z ϵ C`
Let `z_1​=x+iy` and `z_2​=x−iy`
For One-one function :-
`∣z1​∣=x2+y2`
`​∣z2​∣=x2+y2`
`​∣z1​∣=∣z2​∣`
But `z1​!=z2`
​ Hence, f(z) is not a one-one function.
...
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