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Question

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
¯z2z
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D
2¯zz
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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]

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Properties of Conjugate of a Complex Number
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