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
∴ √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 , cos θ < 0 and sin θ > 0
∴ θ lies in second quadrant.
∴ θ = (π−

π

4

) =

3π

4

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

3π

4

)+isin(

3π

4

)]