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We will calculate the difference between $a−bi$ and $c−di.$ Then, we will compare the obtained expression with $2−4i.$
We want our obtained expression to be equivalent to $2−4i.$ For two complex numbers to be equal, both their $real$ $parts$ and their $imaginary$ $parts$ must be equal.
$(a−c)−(b−d)i=2−4i⇕{-(a−c)=-2-(b−d)=-4 (I)(II) $
In Equation (I) we see that the difference between $a$ and $c$ must be $2.$ Similarly, from Equation (II) we can conclude that the difference between $b$ and $d$ must be $4.$ With this information, we can assign the given numbers, $7,$ $4,$ $3,$ and $6,$ to $a,$ $b,$ $c,$ and $d.$
$a−c=2⇒a=6andc=4b−d=4⇒b=7andd=3 $
Now that we have the values, we can write the statement.
$(a−bi)−(c−di)=2−4i⇓(6−7i)−(4−3i)=2−4i $

$(a−bi)−(c−di)$

Simplify

RemoveParRemove parentheses

$a−bi−(c−di)$

DistrDistribute $-1$

$a−bi−c+di$

CommutativePropAddCommutative Property of Addition

$a−c−bi+di$

FactorOutFactor out $-i$

$a−c−i(b−d)$

AddParAdd parentheses

$(a−c)−i(b−d)$

CommutativePropMultCommutative Property of Multiplication

$(a−c)−(b−d)i$