If z is a complex number satisfying z+3¯¯¯z=5−6i, then the value of Im(¯¯¯z) is
A
−3
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B
3
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C
14
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D
54
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Solution
The correct option is A−3 Given : z+3¯¯¯z=5−6i Let z=a+ib⇒¯¯¯z=a−ib Now, putting in the given equation, we get ⇒a+ib+3(a−ib)=5−6i⇒4a−2ib=5−6i⇒4a=5,−2b=−6⇒a=54,b=3⇒z=54+3i⇒¯¯¯z=54−3i∴Im(¯¯¯z)=−3