Complex Numbers (Lesson 4/5)
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Discussion
Consider the functions f(x)=3sin(x), g(x)=5sin(x+2Οβ). Let h(x)=f(x)+g(x).
Our goal is to write h(x) in the form h(x)=Asin(x+B). Let's walk through how to do this step by step.
(a)
First, show that Im(rcis(ΞΈ)) is a sine function.
Solution:
We use the definition
so
Taking the imaginary part gives
which is exactly a sine function of ΞΈ with amplitude r.
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