Let R and C denote the set of real and complex numbers respectively.The function f:C to Ris defined by f(z)=|z| is:
a)one-one but not onto
b)onto but not one-one
c)both one-one and onto
d)neither one-one nor onto
plzz..answer it as soon as possible...its urgent plzz...
neither one-one nor onto.
domain is complex nmbers set and codomain is real numbers set.
for a complex no. z = a+ib , |z| = √(a2+b2) which is always positive and its range is R+.
range is R+ and codomain is R.
as range not equal to codomain, it is not onto.
we can have many numbers where a2 + b2 = c2 + d2 .
So, though, a+ib not equal to c+id, their modulus will be equal.
one such eg is:
1 +7i and 5+5i they both are different complex numbers, but their modulus is same , i.e, √50.
so, it is not one-one.
hope it helps!