Question

# The system of equations |z−3|=√2 and z (1 + i)+ ¯z (1−i)=6 has

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

## The correct option is B only two solutionsPutting z = x + iy in the given equations, we have (z+¯z)+i(z−¯z)=6i.e.x−y=3…… (1) and |z−3|=√2i.e.(x−3)2+y2=2…… (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

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