To determine the amplitude of a complex number, we need to calculate its magnitude or absolute value. The magnitude of a complex number is the distance from the origin to the point representing the complex number in the complex plane.
In this case, we have the complex number Z = 2√2i - 2√3.
To find the magnitude of Z, we can use the formula:
|Z| = √(Re(Z)^2 + Im(Z)^2),
where Re(Z) represents the real part of Z and Im(Z) represents the imaginary part of Z.
In our case, the real part of Z is 0 (since there is no real part) and the imaginary part is -2√3. Plugging these values into the formula, we get:
|Z| = √(0^2 + (-2√3)^2) = √(0 + 12) = √12 = 2√3.
Therefore, the amplitude or magnitude of the complex number Z = 2√2i - 2√3 is 2√3.