We will calculate the difference between
a−bi and
c−di. Then, we will compare the obtained expression with
2−4i.
(a−bi)−(c−di)
a−bi−(c−di)
a−bi−c+di
a−c−bi+di
a−c−i(b−d)
(a−c)−i(b−d)
(a−c)−(b−d)i
We want our obtained expression to be equivalent to
2−4i. For two 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=6 and c=4b−d=4⇒b=7 and d=3
Now that we have the values, we can write the statement.
(a−bi)−(c−di)=2−4i⇓(6−7i)−(4−3i)=2−4i