1. Calculate ln(-/2) and acos(2).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem Statement:**

1. Calculate \( \ln(-\sqrt{2}) \) and \( \arccos(2) \).

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**Explanation:**

- \( \ln(-\sqrt{2}) \): This expression involves the natural logarithm of a negative number, which is not defined in the real number system. In complex numbers, it's represented using logarithmic properties with imaginary components.
  
- \( \arccos(2) \): The inverse cosine function, \( \arccos(x) \), is only defined for \( -1 \leq x \leq 1 \) in real numbers. Since 2 is outside this range, \( \arccos(2) \) does not have a solution in real numbers and is evaluated using complex analysis.

Both calculations require a complex number approach due to their input values being outside the domain of these functions in real numbers.
Transcribed Image Text:**Problem Statement:** 1. Calculate \( \ln(-\sqrt{2}) \) and \( \arccos(2) \). --- **Explanation:** - \( \ln(-\sqrt{2}) \): This expression involves the natural logarithm of a negative number, which is not defined in the real number system. In complex numbers, it's represented using logarithmic properties with imaginary components. - \( \arccos(2) \): The inverse cosine function, \( \arccos(x) \), is only defined for \( -1 \leq x \leq 1 \) in real numbers. Since 2 is outside this range, \( \arccos(2) \) does not have a solution in real numbers and is evaluated using complex analysis. Both calculations require a complex number approach due to their input values being outside the domain of these functions in real numbers.
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