## Precalculus: Mathematics for Calculus, 7th Edition

$(\sqrt 2,135)$
To do these argument problems we first need to look at the coefficients of both the real and non-real/imaginary parts. Then we approach the problem using our beloved $cis(x) = cos(x) + i(sin(x))$. When we do this we want to match the coefficients to unit circle values. This can be done by multiplying by 1/r which will be part of our final argument in the form (r, theta). So here we have coefficients of (1,-1). When we multiply by $1/\sqrt 2$ we get the unit circle value of ($1/\sqrt 2$,$-1/\sqrt 2$) at 135 degrees. So 1/r is equal to $\sqrt 2$ and theta is 45 degrees so the answer is... $(\sqrt 2,135)$