How do you answer this one.
What is the complex expression for a given alternating current,
$\displaystyle i = 250sin(\omega t - 25 ^ \circ)$
a. 227 + j106
b. 160 - j75
c. 227 - j106
d. 160 + j75
For the current
$\displaystyle A\sin(\omega t + \phi)$
The amplitude is $\displaystyle A$ and phase angle is $\displaystyle \phi$.
For this problem $\displaystyle A = 250$ and $\displaystyle \phi = -25^o$.
I think the complex expression being asked is the one with the given amplitude and phase angle.
This is $\displaystyle a + jb$ with
$\displaystyle a^2 + b^2 = A^2$ and
$\displaystyle b/a = tan(\phi)$
So the answer is closest to (c): $\displaystyle 227 - j106$