I want to calculate the magnitude of the following function:
$x(t)=\dfrac{i}{t}(e^{it}+1)$
I did the following to find the magnitude:
$x(t)=\dfrac{i}{t}(1+\cos t+i \sin t)$
$|x(t)|=\sqrt{\dfrac{\sin^2(t)+1+2 \cos(t)+\cos^2(t)}{t^2}}=\sqrt{\dfrac{2+2\cos(t)}{t^2}}$
I am not sure whether it is the correct way to find the magnitude of a function. I will appreciate any help.
$\endgroup$ 11 Answer
$\begingroup$You are correct.
For the magnitude (absolute value) of a complex number, we have $$|r| = \sqrt {x^2 + y^2}$$ where $x$ is the real part and $y$ is the imaginary part.
EDIT: I double-checked your solution and it is exactly what it's supposed to be, with $\dfrac {\sin t}{t}$ as the real part and $\dfrac {\cos t + 1}{t}$ as the imaginary part.
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