Evaluate e^(ip)+1

Problem

e(i*π)+1

Solution

1. Identify the expression as a component of Euler's identity, which relates complex exponentials to trigonometric functions.

2. Apply Euler's formula, which states that e(i*x)=cos(x)+i*sin(x)

3. Substitute π for x in the formula to find the value of e(i*π)

e(i*π)=cos(π)+i*sin(π)

4. Evaluate the trigonometric functions at π

cos(π)=−1

sin(π)=0

5. Simplify the expression for e(i*π) using these values.

e(i*π)=−1+i(0)

e(i*π)=−1

6. Add 1 to the result as required by the original expression.

−1+1=0

Final Answer

e(i*π)+1=0

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