2 Prove the following function is a bijection Let f CC by f

2. Prove the following function is a bijection. Let f : CC by f(a + bi) = abi for all a + bi C.

Solution

let

f(a1+b1i) = f(a2+b2i)

=>

a1-b1i = a2-b2i

=>

a1 = a2, b1 = b2

=>

f is one-one..............(1)

f(a-ib) = a+ib

=>

f is onto...................(2)

(1),(2) implies

f is bijection

thus proved