Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Multiply the following complex numbers:

(4 - 3i) ⋅ (2 + 6i)

Give your answer in the form a + bi.

Sagot :

GinnyAnswer
To multiply the complex numbers [tex]\( (4 - 3i) \)[/tex] and [tex]\( (2 + 6i) \)[/tex], follow these steps:

1. Use the distributive property (also known as the FOIL method for binomials) to expand the product:

[tex]\[ (4 - 3i) \cdot (2 + 6i) = 4 \cdot 2 + 4 \cdot 6i - 3i \cdot 2 - 3i \cdot 6i \][/tex]

2. Calculate each term individually:

[tex]\[ 4 \cdot 2 = 8 \][/tex]

[tex]\[ 4 \cdot 6i = 24i \][/tex]

[tex]\[ -3i \cdot 2 = -6i \][/tex]

[tex]\[ -3i \cdot 6i = -18i^2 \][/tex]

3. Recall that [tex]\(i^2 = -1\)[/tex], so convert [tex]\( -18i^2 \)[/tex]:

[tex]\[ -18i^2 = -18(-1) = 18 \][/tex]

4. Combine all terms together:

[tex]\[ 8 + 24i - 6i + 18 \][/tex]

5. Simplify the expression by combining like terms:

[tex]\[ (8 + 18) + (24i - 6i) \][/tex]

[tex]\[ 26 + 18i \][/tex]

Therefore, the product of the complex numbers [tex]\( (4 - 3i) \cdot (2 + 6i) \)[/tex] is [tex]\( 26 + 18i \)[/tex].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.