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1 (one)

In calculations with complex numbers you often use the number 1 in the form

where k is an integer.

 

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Explanation

By substitution of φ = π in Euler's formula you get

e^iπ = cos π + i sin π = −1 + i·0 = −1

From this follows

so

 

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Example 1

You can calculate the values of 2ⁱ as

 

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