Pregunta
Select the product \( (4+i)(-2-i) \) in the standard form \( a+b i \)
Ask by Hills Willis. in the United States
Nov 25,2024
Solución de inteligencia artificial de Upstudy
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The product is \( -7-6i \).
Solución
Calculate or simplify the expression \( (4+i)(-2-i) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(4+i\right)\left(-2-i\right)\)
- step1: Calculate:
\(4\left(-2\right)+4\left(-i\right)+i\left(-2\right)+i\left(-i\right)\)
- step2: Multiply:
\(-8-4i-2i+1\)
- step3: Rearrange the terms:
\(-7-6i\)
The product \( (4+i)(-2-i) \) in the standard form is \( -7-6i \).
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Simplifique esta solución Extra Insights
To find the product \( (4+i)(-2-i) \), we can use the distributive property (also known as the FOIL method): \[ (4+i)(-2-i) = 4 \cdot (-2) + 4 \cdot (-i) + i \cdot (-2) + i \cdot (-i) \] Calculating each term: 1. \( 4 \cdot (-2) = -8 \) 2. \( 4 \cdot (-i) = -4i \) 3. \( i \cdot (-2) = -2i \) 4. \( i \cdot (-i) = -i^2 = 1 \), since \( i^2 = -1 \) Now, adding these terms together: \[ -8 - 4i - 2i + 1 = -8 + 1 - 6i \] Combining like terms: \[ -7 - 6i \] Thus, the product \( (4+i)(-2-i) \) in standard form \( a + bi \) is \[ \boxed{-7 - 6i}. \]
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