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1 and Euler's identity
With Euler's identity you can write the number 1 as
Explanation
In calculations with complex numbers you frequently use the equation
where k is an integer. Substitution of φ = π in Euler's formula gives
eiπ = cos π + i sin π = −1 + i·0 = −1
From this follows
so
Example 1
You can see that sin (2π) = 0, as according the definition of the sine holds
Example 2
The values of 2i can be calculated with