Let’s look at some properties of complex numbers, numbers of the form where
and
are real numbers and
. We’ll use these together with Euler’s formula to deduce some trig identities.
First, if , I’m going to call
the real part of
and
the imaginary part. We write
and
; the big goofy symbols are for historical reasons.
Now what if we start squaring ? What is
? Computing, we get
, so
.
Similarly, we can compute that . Check these facts to make sure you understand.
Next time, we’ll use them for something!

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Remembering One Trig Identity « Calculus: Problems and Solutions // July 17, 2009 at 4:15 pm |
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