Question

Using the Taylor series for e^x, sin(x), and cos(x), prove that e^ix = cos(x) + i...

Using the Taylor series for e^x, sin(x), and cos(x), prove that e^ix = cos(x) + i sin(x) (Hint: plug in ix into the Taylor series expansion for e^x . Then separate out the terms which have i in them and the terms which do not.)

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Homework Answers

Answer #1

We have to prove the relation

Expanding the terms of left side then

Seperating the terms with i and without i then we will have now

So we get that

We have used

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