## complex exponential - what Am I missing?

Started by 7 years ago●6 replies●latest reply 7 years ago●160 viewsThe following is from Wikipedia - https://en.wikipedia.org/wiki/Euler%27s_formula

below is what I get when I try for 0 and 30 deg

>> sqrt(cos(0)+sin(0))

ans = 1

>> sqrt(cos(30*2*pi/360)+sin(30*2*pi/360))

ans = 1.1688

Should I not be expecting ans = 1 for every value of theta?

Hi. To reinforce what UliBru wrote, your

sqrt(cos(30*2*pi/360)+sin(30*2*pi/360))

command should be changed to:

sqrt(cos(30*2*pi/360)^2 + sin(30*2*pi/360)^2)

Apologies. That was really stupid of me

Sharan123, don't worry. The only people who never makes mistakes are people who never do anything. :-)

If your goal is to understand Euler's equation, you might find my first blog article helpful:

"The Exponential Nature of the Complex Unit Circle"

https://www.dsprelated.com/showarticle/754.php

Cedron,

Thanks. I will take a look.

The basic formula is

sqr(sin(alpha)) + sqr(cos(alpha)) = 1

Thus the correct formula for your example is

sqrt(sqr(sin(alpha)) + sqr(cos(alpha))) = 1