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Application of inequalities and absolute values

If a + ib =...

Question

If $a + i b = c + i d$ , then

a - c = i (b - d)

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a - i b = c - i d

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a = d, b = c

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None of these

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Solution

The correct options are
A $a - c = i (b - d)$
B $a - i b = c - i d$
If $a + i b = c + i d$ .
Equating real and imaginary parts,we get
$a = c$ and $b = d$
$\Rightarrow - b = - d$ .
Therefore $a - i b = c - i d$
Hence, both options A and B are correct.

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