Let V (t) = 15 cos(300t). Express this function in terms of complex exponentials (involving t)
Question
Let V (t) = 15 cos(300t).
Express this function in terms of complex exponentials (involving t)
Solution
The function V(t) = 15 cos(300t) can be expressed in terms of complex exponentials using Euler's formula, which states that e^(ix) = cos(x) + i*sin(x).
Step 1: Write the function in terms of Euler's formula.
V(t) = 15 Re[e^(i300t)]
Step 2: Use the property that the real part of a complex number is equal to half the sum of the number and its complex conjugate.
V(t) = 15/2 [e^(i300t) + e^(-i300t)]
So, the function V(t) = 15 cos(300t) can be expressed in terms of complex exponentials as V(t) = 15/2 [e^(i300t) + e^(-i300t)].
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