wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let C be the set of complex numbers. Prove that the mapping f:CR given by f(z)=|z|, zC, is neither one-one nor onto.

Open in App
Solution

The mapping f:CR is given byf(z)=|z|,zC

Now, f(1)=|1|=1f(1)=|1|=1f(1)=f(1)
Clearly, f 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).


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Animal Tissues
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon