Answer:
Step-by-step explanation:
D. \( x = -2 \) and \( y = 8 \)
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To solve the equation
(
−
7
+
3
)
+
(
−
)
=
(
−
5
+
9
)
(−7+3i)+(x−yi)=(−5+9i), we need to equate the real parts and the imaginary parts separately.
Given:
(
−
7
+
3
)
+
(
−
)
=
(
−
5
+
9
)
(−7+3i)+(x−yi)=(−5+9i)
First, equate the real parts:
−
7
+
=
−
5
−7+x=−5
Solve for
x:
=
−
5
+
7
x=−5+7
=
2
x=2
Next, equate the imaginary parts:
3
−
=
9
3i−yi=9i
Combine like terms involving
i:
(
3
−
)
=
9
(3−y)i=9i
Now, equate the coefficients of
i:
3
−
=
9
3−y=9
Solve for
y:
−
=
9
−
3
−y=9−3
−
=
6
−y=6
=
−
6
y=−6
Therefore, the values of
x and
y are
=
2
x=2 and
=
−
6
y=−6.
So, the correct answer is A.
=
2
x=2 and
=
−
6
y=−6.