I’m having a little hard time understanding the equation:
Why Euler’s relation’s square is equal to 1?
I know how to write Euler’s equation in terms of sin and cos:
But when I do the math, the square of this equality is nothing but 1. I can’t get rid of from the sin and cos in the equation:
I’m probably missing something with the Euler’s relation here so I would like to hear what am I missing.
Notice, that ?x?R:
So, for your integral we get:
?T00|exp(?0tj)|2 dt=?T00|cos(?0t)+sin(?0t)j|2 dt=
?T00(?cos2(?0t)+sin2(?0t)?= 1)2 dt=?T00(?1)2?= 1 dt=
I believe the vertical bars inside the integration denote magnitude. This exponent is a phasor whose magnitude is one and angle is (wt). The square of one is also one.
The magnitude of the phasor (or complex number) is the square root of: the real part squared plus the imaginary part (without j) squared. When you add sin^2 and cos^2, the result is one.
Hope this helps.