Question
If $$\left( {1 + i} \right)z = \left( {1 - i} \right)\overline z $$ then $$z$$ is
A.
$$t\left( {1 - i} \right),t \in R$$
B.
$$t\left( {1 + i} \right),t \in R$$
C.
$$\frac{t}{{1 + i}},t \in {R^ + }$$
D.
None of these
Answer :
$$t\left( {1 - i} \right),t \in R$$
Solution :
$$\eqalign{
& \left( {1 + i} \right)\left( {x + iy} \right) = \left( {1 - i} \right)\left( {x - iy} \right) \cr
& \Rightarrow \,\,\left( {x - y} \right) + i\left( {x + y} \right) = \left( {x - y} \right) - i\left( {x + y} \right) \cr
& \therefore \,\,x + y = 0 \cr
& \therefore \,\,z = x - ix = x\left( {1 - i} \right). \cr} $$