Answer
Step 1. See figure.
Step 2. $\sqrt 2cos(\frac{7\pi}{4})+i\sqrt 2sin(\frac{7\pi}{4})$
Work Step by Step
Step 1. Given the complex number $1-i$, we can identify $a=1, b=-1$ given $(1,-1)$ in complex coordinates as shown in the figure.
Step 2. Using the above results, we can get the modulus as $r=\sqrt {a^2+b^2}=\sqrt {1^2+(-1)^2}=\sqrt 2$. The polar angle can be found as $tan\theta=\frac{b}{a}=-1$, which gives $\theta=\frac{7\pi}{4}$ (in quadrant IV).
Thus, we can write the complex number in polar form as $1-i=\sqrt 2cos(\frac{7\pi}{4})+i\sqrt 2sin(\frac{7\pi}{4})$
