Question

z1 = 1+i , z2 = 2-3i. verify the following of (z1÷z2)bar = z1 bar ÷ z2 bar​

Answer 1

Z1= 1+i

z2= 2-3i

To prove:

(z1÷z2)'= z1'÷ z2'

Proof:

LHS:

(1+i/2-3i)'

On rationalization

We get,

LHS as {( -1+ 5i)/13}'

after conjugating we get LHS as

(-1-5i)/13

Now,

RHS

(1-i)÷(2+3i)

on rationalization

We get RHS as (-1-5i)/13

Since LHS = RHS

Hence Proved