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ఓ 1.8.4 Quiz: Multiplying and Dividing Complex Numbers
Question 8 of 10
Find the product of these complex numbers.
\[
(7+5 i)(-6+9 i)=
\]
A. $3-93 i$
B. $-87-93 i$
C. $-87+33 i$
D. $3+33 i$
Answer
\(\boxed{-87+33 i}\) is the final answer, which corresponds to option C.
Step 1 ：Let's denote the first complex number as a = (7+5i) and the second complex number as b = (-6+9i).
Step 2 ：We multiply the two complex numbers just like we would multiply binomials. We distribute each term in the first complex number to each term in the second complex number and then combine like terms.
Step 3 ：The real parts (those without i) will combine, and the imaginary parts (those with i) will combine. Remember that i^2 = -1.
Step 4 ：After performing the multiplication, we find that the product of a and b is (-87+33i).
Step 5 ：\(\boxed{-87+33 i}\) is the final answer, which corresponds to option C.
