Math Problem Statement
(Cos x+i sin x)^4/(sin x+ i cos x)^5
Solution
The given expression is:
To simplify this expression, let's break it down step by step.
Step 1: Use Euler's formula
Euler's formula states that:
So, we can rewrite the expression as:
Step 2: Simplify the powers
This simplifies to:
Step 3: Distribute the exponent
Step 4: Use Euler's formula again
Using Euler's formula in reverse, we get:
Thus, the simplified expression is:
Final Answer
Would you like more details or have any questions?
- How can Euler's formula be applied to other trigonometric expressions?
- What is the significance of the angle in this context?
- How would the expression change if the powers were different?
- Can you solve a similar problem involving different trigonometric functions?
- How does this concept relate to the complex plane?
Tip: Euler's formula is a powerful tool in complex analysis, connecting trigonometric functions with exponential functions.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Trigonometry
Euler's Formula
Formulas
Euler's formula: e^{ix} = \cos x + i \sin x
Theorems
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Suitable Grade Level
Undergraduate