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.

now,

for a complex no. z = a+ib , |z| = √(a²+b²) which is always positive and its range is R⁺.

now,

range is R⁺ and codomain is R.

as range not equal to codomain, it is not onto.

moreover.

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!