Answer
$$\sqrt 2 \left( {\cos 315^\circ + i\sin 315^\circ } \right)$$
Work Step by Step
$$\eqalign{
& {\text{Rectangular Form }}1 - i \cr
& {\text{Use }}r = \sqrt {{a^2} + {b^2}} {\text{ and }}\theta = {\tan ^{ - 1}}\left( {\frac{b}{a}} \right),{\text{ so}} \cr
& r = \sqrt {{{\left( 1 \right)}^2} + {{\left( { - 1} \right)}^2}} = \sqrt 2 \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{ - 1}}{1}} \right) + 360^\circ \cr
& \theta = 315^\circ \cr
& {\text{write the vector in the trigonometric form }}r\left( {\cos \theta + i\sin \theta } \right) \cr
& = \sqrt 2 \left( {\cos 315^\circ + i\sin 315^\circ } \right) \cr} $$
