Question
If $$z$$ is a complex number satisfying the relation $$\left| {z + 1} \right| = z + 2\left( {1 + i} \right)$$ then $$z$$ is
A.
$$\frac{1}{2}\left( {1 + 4i} \right)$$
B.
$$\frac{1}{2}\left( {3 + 4i} \right)$$
C.
$$\frac{1}{2}\left( {1 - 4i} \right)$$
D.
$$\frac{1}{2}\left( {3 - 4i} \right)$$
Answer :
$$\frac{1}{2}\left( {1 - 4i} \right)$$
Solution :
If $$z = x + iy,\sqrt {{{\left( {x + 1} \right)}^2} + {y^2}} = x + 2\,{\text{and }}0 = y + 2.$$