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1 (one)

The absolute value of the complex number z = r · e with r = 1 is

|e| = 1

 


Explanation

You can show the unit complex numbers in a circle the complex plane. All points on this circle group conform to Euler's formula

e = cos φ + i sin φ

and therefor they give the points shown in the Argand diagram.

Substitution of φ in the formula gives the values

As the only real values are 1 and –1, the absolute value is 1.

 


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