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$a+i b \gt c+i d$ can be explained only when
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The correct answer is:
$b=0, d=0$
$a+i b \gt c+i d$, it is defined if and only if imaginary parts must be equal to zero.
Therefore $i b=i d=0 \Rightarrow b=d=0 \quad(i \neq 0)$
Therefore $i b=i d=0 \Rightarrow b=d=0 \quad(i \neq 0)$
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