To find the amplitude and modulus of the complex number I/(1-i), we first need to express it in the form a + bi, where a is the real part and b is the imaginary part.
Given I/(1-i), let's rationalize the denominator:
I/(1-i) = (I/(1-i)) * ((1+i)/(1+i)) = (I * (1+i)) / ((1-i) * (1+i)) = (I + Ii + Ii - i) / (1 - i + i - i^2) = (I + 2Ii - i) / (1 + 1) = (I - i + 2Ii) / 2 = (I - i) / 2 + Ii.
Now, we can see that the real part, a, is (I - i) / 2, and the imaginary part, b, is I.
The amplitude (or argument) of a complex number is the angle it forms with the positive real axis in the complex plane. We can calculate the amplitude using the formula:
amplitude = arctan(b / a).
In our case, b = I and a = (I - i) / 2. Plugging these values into the formula, we get:
amplitude = arctan(I / ((I - i) / 2)).
The modulus (or magnitude) of a complex number is the distance from the origin to the point representing the complex number in the complex plane. We can calculate the modulus using the formula:
modulus = sqrt(a^2 + b^2).
In our case, a = (I - i) / 2 and b = I. Plugging these values into the formula, we get:
modulus = sqrt(((I - i) / 2)^2 + I^2).
Now, let's simplify these expressions:
amplitude = arctan(I / ((I - i) / 2)), modulus = sqrt(((I - i) / 2)^2 + I^2).
It's important to note that the specific values of I and i were not provided in the question. If I represents the imaginary unit, and i represents a variable or constant, the expressions can be further simplified.