Given complex number, -1 - i |z|=r=√(−1)2+(−1)2 =√2 Now, −1−i can be represented as point P(−1,−1), which lies in 3 rd quadrant.
Now, θ=−π+tan−1(
Im(z)
Re(z)
) = -π + π/4 = -3π/4 ∴ Polar form: z = √2 (cos(-3π/4) + i sin(-3π/4)) = √2 (cos(3π/4) - i sin(3π/4)) (∵ cos (-θ) = cos θ and sin (-θ) =-sin θ) Hence, option (2) is correct.