Pregunta
mplify the expression to \( a+b i \) form: \[ \sqrt{144}-\sqrt{-64}-\sqrt{64}+\sqrt{-49} \]
Ask by Hampton Schwartz. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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The expression simplifies to \( 4 - i \).
Solución
We start with the given expression:
√144 - √(-64) - √64 + √(-49).
1. Simplify each term:
• √144 = 12.
• √(-64) = √64 · i = 8i.
• √64 = 8.
• √(-49) = √49 · i = 7i.
2. Substitute back into the expression:
12 - 8i - 8 + 7i.
3. Combine like terms:
Real part: 12 - 8 = 4.
Imaginary part: -8i + 7i = -i.
Thus, the expression simplifies to 4 - i, which is in a + bi form.
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Simplifique esta solución The Deep Dive
Let's break it down step by step to simplify the expression to \( a + b i \) form: 1. Calculate \(\sqrt{144}\): \[ \sqrt{144} = 12 \] 2. Calculate \(\sqrt{-64}\): \[ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \] 3. Calculate \(\sqrt{64}\): \[ \sqrt{64} = 8 \] 4. Calculate \(\sqrt{-49}\): \[ \sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i \] Now, put it all together in the expression: \[ \sqrt{144}-\sqrt{-64}-\sqrt{64}+\sqrt{-49} = 12 - 8i - 8 + 7i \] Combine the real parts and the imaginary parts: \[ (12 - 8) + (-8i + 7i) = 4 - i \] Thus, the expression simplifies to: \[ \boxed{4 - i} \]
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