Answer :
Final answer:
Performing the operation and simplifying complex numbers.Found by distributing the terms in (1+12i) with those in (9-5i), simplifying, and combining like terms.The correct answer is d) -69 - 63i.
Explanation:
To multiply two complex numbers, like (1+12i) and (9-5i), you distribute each term in the first complex number by each term in the second complex number. This is similar to the FOIL method used for binomials. Therefore, you calculate as follows:
(1)(9) = 9
(1)(-5i) = -5i
(12i)(9) = 108i
(12i)(-5i) = -60i2
To find the product of (1+12i) and (9-5i):
- Multiply the real parts: 1 * 9 = 9
- Multiply the imaginary parts: 12i * -5i = -60i² = 60
- Combine the results: 9 + 60 = 69, giving -69; 0 + (12) * (-5) = -60, giving -63i.
Therefore, the product of (1+12i) and (9-5i) simplifies to -69 - 63i.
The correct answer is d) -69 - 63i.
