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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].
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