We have, z = 1 – i
Let 1 = r cosθ…(i)
and – 1 = r sinθ …(ii)
Squaring and adding (i) and (ii), we get
r2(cos2θ+sin2θ) = 1 + 1 ⇒ r2 = 2 ⇒ r = √2
Substituting the value of r in (i) and (ii), we get √2 cos θ = 1 , √2 sin θ = - 1
⇒ cos θ =

1

√2

, sin θ = −

1

√2

⇒ cos θ = cos

π

4

, sin θ = - sin

π

4

Here, cosθ > 0 and sinθ < 0.
∴ θ lies in the fourth quadrant.
∴ θ = −

π

4

∴ The required polar form is
z = √2(cos(−

π

4

)+isin(−

π

4

))