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Question

If z is a complex number satisfying z+3¯¯¯z=56i, 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=56i
Let z=a+ib¯¯¯z=aib
Now, putting in the given equation, we get
a+ib+3(aib)=56i4a2ib=56i4a=5, 2b=6a=54,b=3z=54+3i¯¯¯z=543iIm(¯¯¯z)=3

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