Question

I apologize if this question is too much to ask on this site, but I am really confused. Any help would be greatly appreciated.

The famous formula shown below is called Euler’s formula, after the Swiss mathematician Leonhard Euler (1707-1783).

e^(a + bi) = e^(a)(cos b + i sin b)

This formula gives rise to the equation e^(πi) + 1 = 0. This equation related the five most famous numbers in mathematics--0, 1,π , e, and i-- in a single equation. Show how Euler’s formula can be used to derive this equation. Write a short paragraph summarizing your work.

Answer 1

e^(0 + pi i) = e^0 (cos pi + i sin pi)

= 1 (-1 +0 )
= -1

so
e^(i pi ) =-1
or
e^(i pi) + 1 =0