Question

The system of equations $|z-3|=\sqrt{2}$ and z (1 + i)+ $\overline{z}(1-i)=6$ has

• A. no solution
• B. infinitely many solutions
• C. only two solutions
• D. Only one solution

Answer 1

The correct option is C only two solutions

Putting z = x + iy in the given equations, we have
$(z+\overline{z})+i(z-\overline{z})=6i.e.x-y=3\dots \dots$ (1)
and $|z-3|=\sqrt{2}i.e.(x-3{)}^2+y^2=2\dots \dots$ (2)
Solving equations (1) and (2), we have y = -1, 1 and corresponding x = 2, 4 Hence, there are only two solutions, viz.
z = 2 - I, 4 + i