If z is a complex number, then the conjugate of z+2¯z is
A
2¯z+z
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B
¯z+2z
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C
¯z−2z
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D
2¯z−z
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Solution
The correct option is B¯z+2z By property of conjugates, we know that, [¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2=¯¯¯¯¯z1+¯¯¯¯¯z2] ∴¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(z+2¯¯¯z)=¯¯¯z+¯¯¯¯¯¯¯¯¯¯(2¯z)=¯¯¯z+2¯¯¯¯¯¯z[∵¯¯¯¯¯¯¯¯¯¯¯¯¯¯(z1z2)=¯¯¯¯¯z1¯¯¯¯¯z2,¯¯¯2=2]=¯¯¯z+2z[∵¯¯¯¯¯¯z=z]