Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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].
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].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.