Wright State University Lake Campus/2020-1/Intro to imaginary numbers

Students have trouble appreciating the square root of minus 1, or

\sqrt{- 1} = i

For this introduction, all you need is the following ideas:

\frac{d}{d t} C t^{n} = n C t^{n - 1}

F = - k x = m a = m \frac{d v}{d t} = m \frac{d^{2} x}{d t^{2}}

The first step in understanding the solution to this is to imagine that k=m=1:

\frac{d^{2} x}{d t^{2}} = - x

What function of time is the negative of it's own derivative?

The following infinite series famously equals it's own second derivative:

f (t) = 1 + t + \frac{1}{2 \cdot 1} t^{2} + \frac{1}{2 \cdot 1} t^{2} + \frac{1}{3 \cdot 2 \cdot 1} t^{3} + \frac{1}{4 \cdot 3 \cdot 2 \cdot 1} t^{4} + . . .

See

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